Finite Group Databasebeta

← #16726553

Subgroups — #16726553

Order 3328.

2666 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719455C211yesmaximal, characteristic
2C2×D13×#131C211yesmaximal, characteristic
3#13128035C211yesmaximal, characteristic
4#13123405C213yesmaximal, complemented
5#13123404C211yesmaximal, characteristic, complemented
6#13123403C213yesmaximal, complemented
7#13123403C213yesmaximal, complemented
8#13123402C211yesmaximal, characteristic, complemented
9#13123402C211yesmaximal, characteristic, complemented
10#13123401C213yesmaximal, complemented
11#13123398C213yesmaximal, complemented
12#13123397C213yesmaximal, complemented
13C2×#11718500C213yesmaximal, complemented
14D13×#424C213yesmaximal, complemented
15C13×#2906C211yesmaximal, characteristic, complemented
16C2×#41×D13C2211yescharacteristic
17C2×C13×#131C2211yescharacteristic
18C2×C13×#131C2211yescharacteristic
19C4×C13×#41C2211yescharacteristic
20#41×Dic13C2211yescharacteristic
21C2×#88202C2211yescharacteristic
22C2×#88202C2211yescharacteristic
23#11719455—28no—
24D13×#131—28no—
25C2×#88161C2213yes—
26C2×#88161C2213yes—
27C2×M16×D13C2213yes—
28C2×M16×D13C2213yes—
29C2×#88155C2213yes—
30C2×#88155C2213yes—
31C22×#6094C2213yes—
32C22×C8×D13C2213yes—
33#11719279C411yescharacteristic
34#11719279C411yescharacteristic
35#11719277C411yescharacteristic
36#11719277C411yescharacteristic
37#11719251C413yes—
38#11719251C413yes—
39#11719250C413yes—
40#11719250C413yes—
41#11719227C2213yes—
42D13×#117C2213yes—
43C4×#6127C2213yes—
44C2×#88126C2213yes—
45C13×#424C2213yescomplemented
46C13×#424C2213yescomplemented
47C13×#423C2213yescomplemented
48C2×C13×C4⋊C8C2213yescomplemented
49#11718780C2213yescomplemented
50#11718780C2213yescomplemented
51#11718779C2213yescomplemented
52#11718779C2213yescomplemented
53#11718763C2213yescomplemented
54#11718763C2213yescomplemented
55C2×#88054C2213yescomplemented
56C2×#88054C2213yescomplemented
57#11718660C2213yescomplemented
58#11718660C2213yescomplemented
59#11718585C2213yescomplemented
60C2×C4⋊#1055C2213yescomplemented
61#11718500C2213yes—
62#11718500C2216yes—
63#11718500C2211yescharacteristic
64#11718500C2213yes—
65#11718500C2213yes—
66#11718500C2213yescomplemented
67#11718500C2213yescomplemented
68#11718500C2213yescomplemented
69#11718500C2213yescomplemented
70#11718500C2216yescomplemented
71#11718500C2216yescomplemented
72#11718498C2216yescomplemented
73#11718498C2216yescomplemented
74D13×C4⋊C8C2216yescomplemented
75D13×C4⋊C8C2216yescomplemented
76C2×C13×#41C2311yescharacteristic
77#41×D13D418yes—
78#41×D13Q818yes—
79C2×#6131C2×C411yescharacteristic
80C2×Q8×D13C2×C411yescharacteristic
81C2×#6129C2×C413yes—
82C2×D4×D13C2×C413yes—
83C2×#6127C2313yes—
84C22×C4×D13C2313yes—
85C13×#131—24no—
86C13×#131—24no—
87C2×C13×M16C2313yes—
88C2×C13×M16C2313yes—
89C22×C8×C13C2313yes—
90C22×C8×C13C2313yes—
91C4×Q8×C13C2×C411yescharacteristic
92C4×Q8×C13C2×C411yescharacteristic
93C4×D4×C13C2×C413yes—
94C4×D4×C13C2×C413yes—
95C13×#117C2313yes—
96C2×C42×C13C2313yes—
97#88202—24no—
98#88202—24no—
99Q8×Dic13C2×C411yescharacteristic
100Q8×Dic13C2×C411yescharacteristic
101D4×Dic13C2×C413yes—
102D4×Dic13C2×C413yes—
103C4×C22⋊D13C2×C416yes—
104C4×C22⋊D13C2×C416yes—
105C2×#6103C2×C413yes—
106C2×#6103C2×C413yes—
107#88180C2313yes—
108C2×#6101C2×C413yes—
109C2×#6101C2×C413yes—
110C2×C4×Dic13C2313yes—
111C2×#6099C2313yes—
112C2×#6099C2313yes—
113C22×#1055C2313yes—
114C22×#1055C2313yes—
115#88161—212no—
116#88161—212no—
117M16×D13—212no—
118M16×D13—212no—
119#88155—212no—
120#88155—212no—
121C2×#6094—212no—
122C2×#6094C2311yescharacteristic
123C2×#6094C2313yes—
124C2×#6094C2313yes—
125C2×#6094C2313yes—
126C2×#6094C2316yes—
127C2×C8×D13—212no—
128C2×C8×D13C2311yescharacteristic
129C2×C8×D13C2313yes—
130C2×C8×D13C2313yes—
131C2×C8×D13C2313yes—
132C2×C8×D13C2316yes—
133#88147C2×C413yes—
134#88147C2×C413yes—
135#88146C2×C413yes—
136#88146C2×C413yes—
137C4⋊C4×D13C2×C413yes—
138C4⋊C4×D13C2×C413yes—
139#88141C2×C413yes—
140#88141C2×C413yes—
141#88135C2×C416yes—
142#88135C2×C416yes—
143C22⋊C4×D13C2×C416yes—
144#88131C2×C416yes—
145C4×D52C2×C413yes—
146C4×D52C2×C413yes—
147#88126C2×C413yes—
148#88126C2×C413yes—
149#88126C2×C413yes—
150#88126C2×C413yes—
151#88126C2311yescharacteristic
152#88126C2313yes—
153#88126C2313yes—
154#88126C2313yes—
155C42×D13C2316yes—
156C4×Dic26C2×C413yes—
157C4×Dic26C2×C413yes—
158C13×C4⋊C8C2311yescharacteristic
159C13×C4⋊C8C2313yes—
160C13×C4⋊C8C2313yes—
161C13×C4⋊C8C2313yes—
162C13×C4⋊C8C2316yes—
163#88054C2313yes—
164#88054C2313yes—
165#88054C2316yes—
166#88054C2316yes—
167#88054C2313yes—
168#88054C2313yes—
169#88054C2311yescharacteristic
170#88054C2311yescharacteristic
171#88054C2313yes—
172#88054C2313yes—
173C4⋊#1055C2313yes—
174C4⋊#1055C2316yes—
175C4⋊#1055C2313yes—
176C4⋊#1055C2311yescharacteristic
177C4⋊#1055C2313yes—
178#60100—131nomaximal, Sylow
179C23×D13C22×C413yes—
180C13×#41C2×D414yes—
181C13×#41C2×Q814yes—
182C2×Q8×C13C22×C411yescharacteristic
183C2×D4×C13C22×C413yes—
184C22×C4×C13C22×C413yes—
185C22×C4×C13C22×C413yes—
186C22×C4×C13C2413yes—
187C2×C22⋊D13C22×C416yes—
188C22×Dic13C22×C413yes—
189C22×Dic13C22×C413yes—
190C22×Dic13C22×C413yes—
191#6131C4⋊C418yes—
192Q8×D13C4⋊C418yes—
193#6129C4⋊C4124yes—
194D4×D13C4⋊C4124yes—
195#6127C2×D4112yes—
196#6127C2×Q8112yes—
197C2×D52C22×C413yes—
198C2×C4×D13C22×C416yes—
199C2×C4×D13C22×C416yes—
200C2×C4×D13C22×C413yes—
201C2×C4×D13C22×C413yes—
202C2×C4×D13C2×D4112yes—
203C2×C4×D13C2×Q8112yes—
204C2×C4×D13C2413yes—
205C2×C4×D13C2411yescharacteristic
206C2×Dic26C22×C413yes—
207C13×M16—26no—
208C13×M16—26no—
209C2×C8×C13—26no—
210C2×C8×C13—26no—
211C2×C8×C13C2411yescharacteristic
212C2×C8×C13C2413yes—
213C2×C8×C13C2413yes—
214C2×C8×C13C2411yescharacteristic
215C13×C4⋊C4C22×C413yes—
216C13×C4⋊C4C22×C413yes—
217C13×C22⋊C4C22×C416yes—
218C42×C13C22×C413yes—
219C42×C13C22×C413yes—
220C42×C13C2413yes—
221C42×C13C2411yescharacteristic
222C22⋊Dic13C22×C416yes—
223#6103C22×C411yescharacteristic
224#6103C22×C411yescharacteristic
225#6103C22×C413yes—
226#6103C22×C413yes—
227#6103C22×C413yes—
228#6103C22×C413yes—
229#6103C22×C413yes—
230#6103C22×C413yes—
231C4⋊Dic13C22×C413yes—
232C4⋊Dic13C22×C413yes—
233#6101C22×C413yes—
234#6101C22×C413yes—
235#6101C22×C411yescharacteristic
236#6101C22×C411yescharacteristic
237#6101C22×C413yes—
238#6101C22×C413yes—
239#6101C22×C413yes—
240#6101C22×C413yes—
241C4×Dic13C22×C416yes—
242C4×Dic13C22×C416yes—
243C4×Dic13C22×C413yes—
244C4×Dic13C22×C413yes—
245C4×Dic13C2413yes—
246C4×Dic13C2411yescharacteristic
247#6099—26no—
248#6099—26no—
249C2×#1055—26no—
250C2×#1055—26no—
251C2×#1055C2411yescharacteristic
252C2×#1055C2413yes—
253C2×#1055C2413yes—
254C2×#1055C2411yescharacteristic
255#6094—22no—
256#6094—26no—
257#6094—26no—
258#6094—26no—
259#6094—212no—
260C8×D13—22no—
261C8×D13—26no—
262C8×D13—26no—
263C8×D13—26no—
264C8×D13—212no—
265C2×#568—131no—
266C22×#131—131no—
267#3428—131no—
268#2906—133no—
269#2906—133no—
270#2906—133no—
271#2906—133no—
272#2906—131no—
273#2906—131no—
274#2906—131no—
275#2906D1311yescharacteristic, complemented
276#2905—133no—
277#2905—133no—
278C2×#424—133no—
279C2×#424—133no—
280C23×C13C23×C413yes—
281C22×D13—43no—
282C22×D13—43no—
283C22×D13C2×C4⋊C4112yes—
284C22×D13C23×C411yescharacteristic
285C22×D13C23×C413yes—
286Q8×C13C2×C4⋊C414yes—
287D4×C13C2×C4⋊C4112yes—
288C2×C4×C13—43no—
289C2×C4×C13—43no—
290C2×C4×C13C23×C413yes—
291C2×C4×C13C23×C413yes—
292C2×C4×C13C23×C411yescharacteristic
293C2×C4×C13C23×C411yescharacteristic
294C2×C4×C13C23×C413yes—
295C2×C4×C13C22×D416yes—
296C2×C4×C13C22×Q816yes—
297C2×C4×C13C2511yescharacteristic
298C22⋊D13C2×C4⋊C4124yes—
299C2×Dic13—43no—
300C2×Dic13—43no—
301C2×Dic13C2×C4⋊C4112yes—
302C2×Dic13C23×C411yescharacteristic
303C2×Dic13C23×C411yescharacteristic
304C2×Dic13C23×C413yes—
305C2×Dic13C23×C413yes—
306C2×Dic13C23×C413yes—
307C2×Dic13C23×C411yescharacteristic
308D52C2×C4⋊C4112yes—
309C4×D13—46no—
310C4×D13—46no—
311C4×D13C2×C4⋊C4112yes—
312C4×D13C2×C4⋊C4112yes—
313C4×D13C22×D412yes—
314C4×D13C22×D416yes—
315C4×D13C22×Q812yes—
316C4×D13C22×Q816yes—
317Dic26C2×C4⋊C4112yes—
318C8×C13—21no—
319C8×C13—23no—
320C8×C13—23no—
321C8×C13—21no—
322#1055—21no—
323#1055—23no—
324#1055—23no—
325#1055—21no—
326C22×#41—131no—
327#568—268no—
328C2×#131—131no—
329C2×#131—131no—
330C2×#131—133no—
331C2×#131—133no—
332C2×#131—133no—
333C2×#131—133no—
334C2×#131—268no—
335C2×#131C2×D1311yescharacteristic
336C2×#131C2×D1311yescharacteristic
337C22×M16—133no—
338C22×M16—133no—
339C22×M16—133no—
340C23×C8—133no—
341#520—131no—
342#520—131no—
343#520—133no—
344#520—133no—
345#519—131no—
346#519—131no—
347#518—133no—
348#518—133no—
349C4×#41—131no—
350C4×#41—133no—
351C4×#41—133no—
352C4×#41C2×D1311yescharacteristic
353C2×#117—133no—
354C2×#117—133no—
355#424—133no—
356#424—133no—
357#424—133no—
358#424—133no—
359#424—133no—
360#424—133no—
361#424—133no—
362#424—131no—
363#424—136no—
364#424—133no—
365#424—133no—
366#424—133no—
367#424—133no—
368#424—133no—
369#424—133no—
370#424—136no—
371#424—136no—
372#424C2×D1313yescomplemented
373#424C2×D1313yescomplemented
374#423—133no—
375#423—133no—
376#423—133no—
377#423—136no—
378#423—136no—
379#423C2×D1313yescomplemented
380C2×C4⋊C8—133no—
381C2×C4⋊C8—133no—
382C2×C4⋊C8—133no—
383C2×C4⋊C8—136no—
384C2×C4⋊C8—136no—
385C2×C4⋊C8C2×D1313yescomplemented
386C22×C13—23no—
387C22×C13—23no—
388C22×C13C22×C4⋊C416yes—
389C22×C13C24×C411yescharacteristic
390C2×D13—23no—
391C2×D13—23no—
392C2×D13—21no—
393C2×D13—21no—
394C2×D13—412no—
395C2×D13C22×C4⋊C412yes—
396C2×D13C22×C4⋊C416yes—
397C4×C13—23no—
398C4×C13—23no—
399C4×C13—21no—
400C4×C13—21no—
401C4×C13C22×C4⋊C416yes—
402C4×C13C23×D411yescharacteristic
403C4×C13C23×Q811yescharacteristic
404Dic13—23no—
405Dic13—23no—
406Dic13—21no—
407Dic13—21no—
408Dic13C22×C4⋊C416yes—
409Dic13C22×C4⋊C412yes—
410C2×#41—138no—
411C2×#41—138no—
412C2×#41—131no—
413C2×#41—133no—
414C2×#41—133no—
415C2×#41C22×D1311yescharacteristic
416C22×Q8—131no—
417C22×D4—133no—
418C23×C4—133no—
419#131—24no—
420#131—24no—
421#131—2612no—
422#131—2612no—
423#131—2612no—
424#131—2612no—
425#131—264no—
426#131—264no—
427C2×M16—133no—
428C2×M16—133no—
429C2×M16—133no—
430C2×M16—131no—
431C2×M16—136no—
432C2×M16—133no—
433C2×M16—133no—
434C2×M16—2612no—
435C2×M16—2612no—
436C2×M16—2612no—
437C2×M16C22×D1313yes—
438C2×M16C22×D1313yes—
439C22×C8—133no—
440C22×C8—133no—
441C22×C8—131no—
442C22×C8—133no—
443C22×C8—133no—
444C22×C8—133no—
445C22×C8—136no—
446C22×C8—2612no—
447C22×C8C22×D1313yes—
448C22×C8C22×D1313yes—
449C4×Q8—131no—
450C4×Q8—131no—
451C4×Q8—133no—
452C4×Q8—133no—
453C4×Q8—133no—
454C4×Q8—133no—
455C4×Q8C4×D1311yescharacteristic
456C4×Q8C4×D1311yescharacteristic
457C4×D4—133no—
458C4×D4—133no—
459C4×D4—136no—
460C4×D4—136no—
461C4×D4—133no—
462C4×D4—133no—
463C4×D4—136no—
464C4×D4—136no—
465C4×D4—133no—
466C4×D4—133no—
467C4×D4C4×D1313yes—
468C4×D4C4×D1313yes—
469#117—133no—
470#117—133no—
471#117—133no—
472#117—136no—
473#117—133no—
474#117—133no—
475#117—133no—
476#117—133no—
477#117—133no—
478#117—131no—
479#117—133no—
480#117—133no—
481#117C22×D1313yes—
482C2×C4⋊C4—133no—
483C2×C4⋊C4—133no—
484C2×C4⋊C4—133no—
485C2×C4⋊C4—133no—
486C2×C22⋊C4—133no—
487C2×C22⋊C4—133no—
488C2×C22⋊C4—136no—
489C2×C42—133no—
490C2×C42—136no—
491C2×C42C22×D1313yes—
492C4⋊C8—133no—
493C4⋊C8—131no—
494C4⋊C8—131no—
495C4⋊C8—133no—
496C4⋊C8—133no—
497C4⋊C8—133no—
498C4⋊C8—133no—
499C4⋊C8—136no—
500C4⋊C8—136no—
501C4⋊C8—133no—
502C4⋊C8—133no—
503C4⋊C8—131no—
504C4⋊C8—133no—
505C4⋊C8—136no—
506C4⋊C8—133no—
507C4⋊C8C22×D1313yes—
508C4⋊C8C22×D1316yes—
509C4⋊C8C22×D1311yescharacteristic
510C4⋊C8C22×D1313yes—
511C4⋊C8C22×D1313yes—
512C2×C13—26no—
513C2×C13C23×C4⋊C411yescharacteristic
514C2×C13#357311yescharacteristic
515C2×C13#357311yescharacteristic
516D13—22no—
517D13—26no—
518C24—133no—
519#41—138no—
520#41—1324no—
521#41—1312no—
522#41—1312no—
523#41D4×D1314yes—
524#41Q8×D1314yes—
525C2×Q8—138no—
526C2×Q8—133no—
527C2×Q8C2×C4×D1311yescharacteristic
528C2×D4—136no—
529C2×D4—1324no—
530C2×D4—133no—
531C2×D4C2×C4×D1313yes—
532C22×C4—133no—
533C22×C4—133no—
534C22×C4—133no—
535C22×C4—1312no—
536C22×C4—1312no—
537C22×C4—133no—
538C22×C4—131no—
539C22×C4—133no—
540C22×C4—133no—
541C22×C4—136no—
542C22×C4—136no—
543C22×C4C2×C4×D1313yes—
544C22×C4C2×C4×D1313yes—
545C22×C4C23×D1313yes—
546M16—26no—
547M16—26no—
548M16—262no—
549M16—266no—
550M16—266no—
551M16—266no—
552M16—2612no—
553M16—266no—
554M16—266no—
555C2×C8—26no—
556C2×C8—26no—
557C2×C8—131no—
558C2×C8—131no—
559C2×C8—133no—
560C2×C8—133no—
561C2×C8—262no—
562C2×C8—266no—
563C2×C8—266no—
564C2×C8—266no—
565C2×C8—2612no—
566C2×C8—266no—
567C2×C8—266no—
568C2×C8C23×D1311yescharacteristic
569C2×C8C23×D1313yes—
570C2×C8C23×D1313yes—
571C2×C8C23×D1311yescharacteristic
572C4⋊C4—133no—
573C4⋊C4—133no—
574C4⋊C4—131no—
575C4⋊C4—131no—
576C4⋊C4—133no—
577C4⋊C4—133no—
578C4⋊C4—133no—
579C4⋊C4—133no—
580C4⋊C4—133no—
581C4⋊C4—133no—
582C4⋊C4C2×C4×D1313yes—
583C4⋊C4C2×C4×D1313yes—
584C22⋊C4—136no—
585C22⋊C4—133no—
586C22⋊C4—133no—
587C22⋊C4—131no—
588C22⋊C4—131no—
589C22⋊C4—133no—
590C22⋊C4—133no—
591C22⋊C4—133no—
592C22⋊C4—133no—
593C22⋊C4C2×C4×D1316yes—
594C42—136no—
595C42—136no—
596C42—133no—
597C42—133no—
598C42—131no—
599C42—133no—
600C42C2×C4×D1313yes—
601C42C2×C4×D1313yes—
602C42C23×D1313yes—
603C42C23×D1311yescharacteristic
604C13#6010011yescharacteristic, complemented, Sylow
605C23—131no—
606C23—133no—
607C23—1312no—
608C23—523no—
609C23—523no—
610C23C22×C4×D1313yes—
611Q8—1312no—
612Q8C4⋊C4×D1314yes—
613D4—1324no—
614D4—1312no—
615D4C4⋊C4×D13112yes—
616C2×C4—43no—
617C2×C4—43no—
618C2×C4—1312no—
619C2×C4—133no—
620C2×C4—131no—
621C2×C4—1312no—
622C2×C4—1312no—
623C2×C4—132no—
624C2×C4—136no—
625C2×C4—132no—
626C2×C4—136no—
627C2×C4—133no—
628C2×C4—131no—
629C2×C4—133no—
630C2×C4—131no—
631C2×C4—526no—
632C2×C4—526no—
633C2×C4—523no—
634C2×C4—523no—
635C2×C4C22×C4×D1313yes—
636C2×C4C22×C4×D1313yes—
637C2×C4C22×C4×D1311yescharacteristic
638C2×C4C22×C4×D1311yescharacteristic
639C2×C4C22×C4×D1313yes—
640C2×C4C2×D4×D1316yes—
641C2×C4C2×Q8×D1316yes—
642C2×C4C24×D1311yescharacteristic
643C8—21no—
644C8—21no—
645C8—23no—
646C8—23no—
647C8—261no—
648C8—263no—
649C8—263no—
650C8—261no—
651C22—23no—
652C22—23no—
653C22—132no—
654C22—136no—
655C22—263no—
656C22—261no—
657C22—263no—
658C22—261no—
659C22—5212no—
660C22C2×C4⋊C4×D1316yes—
661C22C23×C4×D1311yescharacteristic
662C4—21no—
663C4—23no—
664C4—21no—
665C4—23no—
666C4—132no—
667C4—136no—
668C4—263no—
669C4—261no—
670C4—263no—
671C4—261no—
672C4C2×C4⋊C4×D1316yes—
673C4C22×D4×D1311yescharacteristic
674C4C22×Q8×D1311yescharacteristic
675C2—26no—
676C2—262no—
677C2—266no—
678C2C22×C4⋊C4×D1311yescharacteristic
679C2#1312954711yescharacteristic
680C2#1312954911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D13
commutator, socleC22×C13C24×C4
FittingC13×#2906C2
prime radicalC2×#41×D13C22
cosocleC2×C4×C13C25
hypercenter#2906D13
hypocenterC13#60100
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #2906

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #13123405C2semidirect
5. #13123404C2semidirect
6. #13123403C2semidirect
7. #13123403C2semidirect
8. #13123402C2semidirect
9. #13123402C2semidirect
10. #13123401C2semidirect
11. #13123398C2semidirect
12. #13123397C2semidirect
13. C2×#11718500C2semidirect
14. D13×#424C2semidirect
15. C13×#2906C2semidirect
45. C13×#424C22semidirect
46. C13×#424C22semidirect
47. C13×#423C22semidirect
48. C2×C13×C4⋊C8C22semidirect
49. #11718780C22semidirect
50. #11718780C22semidirect
51. #11718779C22semidirect
52. #11718779C22semidirect
53. #11718763C22semidirect
54. #11718763C22semidirect
55. C2×#88054C22semidirect
56. C2×#88054C22semidirect
57. #11718660C22semidirect
58. #11718660C22semidirect
59. #11718585C22semidirect
60. C2×C4⋊#1055C22semidirect
66. #11718500C22semidirect
67. #11718500C22semidirect
68. #11718500C22semidirect
69. #11718500C22semidirect
70. #11718500C22semidirect
71. #11718500C22semidirect
72. #11718498C22semidirect
73. #11718498C22semidirect
74. D13×C4⋊C8C22semidirect
75. D13×C4⋊C8C22semidirect
275. #2906D13semidirect
372. #424C2×D13semidirect
373. #424C2×D13semidirect
379. #423C2×D13semidirect
385. C2×C4⋊C8C2×D13semidirect
604. C13#60100semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117194552
C2×D13×#1312
#131280352
#131234052
#131234042
#131234032
#131234022
#131234012
#131233982
#131233972
C2×#117185002
D13×#4242
C13×#29062
#6010013