Finite Group Databasebeta

← C2×#13126074 #16735078

Subgroups — C2×#13126074 #16735078

Order 3328.

1790 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719222C211yesmaximal, characteristic, complemented
2C2×#11719305C211yesmaximal, characteristic
3#13126074C2116yesmaximal, direct product factor
4C2×#11718537C211yesmaximal, characteristic, complemented
5C2×#11718517C211yesmaximal, characteristic, complemented
6C2×#11718426C211yesmaximal, characteristic, complemented
7C2×#11718426C211yesmaximal, characteristic, complemented
8C2×#11718384C211yesmaximal, characteristic, complemented
9C2×#11718657C211yesmaximal, characteristic, complemented
10C2×#11718696C211yesmaximal, characteristic
11C2×#11718518C211yesmaximal, characteristic, complemented
12C2×#11718538C211yesmaximal, characteristic, complemented
13C2×#11718424C211yesmaximal, characteristic, complemented
14C2×#11718427C211yesmaximal, characteristic, complemented
15C2×#11718380C211yesmaximal, characteristic, complemented
16C2×C13×#482C211yesmaximal, characteristic
17C2×C13×#121C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×#88190C2211yescharacteristic
20C2×#88189—21no—
21C2×D4×Dic13—21no—
22C2×D4×Dic13C2211yescharacteristic
23C2×#88180C2211yescharacteristic
24C2×#88178C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26#11719305—24no—
27#11719305C2218yes—
28#11719222—24no—
29#11719222C2218yescomplemented
30C2×#88144C2211yescharacteristic
31C2×#88144C2211yescharacteristic
32C2×#88144C2211yescharacteristic
33C2×#88142C2211yescharacteristic
34C2×#88142C2211yescharacteristic
35C2×#88141C2211yescharacteristic
36C2×#88133—21no—
37C2×#88132—21no—
38C2×#88132—21no—
39C2×#88131—21no—
40C2×C4×Dic26—21no—
41C2×C4×Dic26—21no—
42C13×#482C2218yes—
43C2×C13×#107C2211yescharacteristic
44C2×C13×#106C2211yescharacteristic
45C2×C13×#102C2211yescharacteristic
46C2×C13×#102C2211yescharacteristic
47C2×C13×C22⋊C8C2211yescharacteristic
48C2×#88072C2211yescharacteristic
49C2×#88072C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51C2×#88058C2211yescharacteristic
52C2×#88057C2211yescharacteristic
53C2×#88056C2211yescharacteristic
54C2×#88056C2211yescharacteristic
55C2×#88055C2211yescharacteristic
56C2×#88055C2211yescharacteristic
57C2×#88054C2211yescharacteristic
58C2×#88054C2211yescharacteristic
59#11718696C2218yes—
60#11718657C2218yescomplemented
61C2×#88050C2211yescharacteristic
62C2×#88050C2211yescharacteristic
63C2×#88048C2211yescharacteristic
64C2×#88048C2211yescharacteristic
65C2×#88047C2211yescharacteristic
66C2×#88047C2211yescharacteristic
67#11718538C2218yescomplemented
68#11718537C2218yescomplemented
69#11718518C2218yescomplemented
70#11718517C2218yescomplemented
71#11718427C2218yescomplemented
72#11718426C2218yescomplemented
73#11718426C2218yescomplemented
74#11718424C2218yescomplemented
75#11718384C2218yescomplemented
76#11718380C2218yescomplemented
77C22×D4×C13—21no—
78C22×D4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×Dic13—21no—
81C23×Dic13D411yescharacteristic
82C23×Dic13D411yescharacteristic
83C22×Dic26—21no—
84C22×Dic26—21no—
85C22×Dic26C2311yescharacteristic
86C22×C8×C13C2311yescharacteristic
87C22×C8×C13C2311yescharacteristic
88C13×#121—22no—
89C13×#121C2314yes—
90C13×#117—22no—
91C13×#117C2314yes—
92C2×C13×C4⋊C4C2311yescharacteristic
93C2×C13×C4⋊C4C2311yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—21no—
97C2×C42×C13—21no—
98C2×C22⋊Dic13—21no—
99C2×C22⋊Dic13—21no—
100C2×C22⋊Dic13—21no—
101C2×C22⋊Dic13—21no—
102C2×C22⋊Dic13—21no—
103#88190—22no—
104#88190C2314yes—
105#88189—28no—
106D4×Dic13—28no—
107D4×Dic13—22no—
108D4×Dic13C2314yes—
109#88180—22no—
110#88180C2314yes—
111C2×C4⋊Dic13—21no—
112C2×C4⋊Dic13—21no—
113C2×C4⋊Dic13—21no—
114C2×C4⋊Dic13C2311yescharacteristic
115C2×C4⋊Dic13C2311yescharacteristic
116C2×C4⋊Dic13C2311yescharacteristic
117#88178—22no—
118#88178C2314yes—
119C2×#6101—21no—
120C2×#6101—21no—
121C2×#6101—21no—
122C2×#6101—21no—
123C2×#6101—21no—
124C2×#6101—21no—
125C2×#6101—21no—
126C2×C4×Dic13—21no—
127C2×C4×Dic13—21no—
128C2×C4×Dic13D411yescharacteristic
129C2×C4×Dic13D411yescharacteristic
130C2×C4×Dic13D414yes—
131C2×C4×Dic13C2311yescharacteristic
132C2×C4×Dic13C2311yescharacteristic
133C2×C4×Dic13C2314yes—
134C22×#1055C2311yescharacteristic
135C22×#1055C2311yescharacteristic
136#88144—22no—
137#88144—22no—
138#88144—22no—
139#88144C2314yes—
140#88144C2314yes—
141#88144C2314yes—
142#88142—22no—
143#88142—22no—
144#88142C2314yes—
145#88142C2314yes—
146#88141—22no—
147#88141C2314yes—
148#88133—28no—
149#88132—28no—
150#88132—28no—
151#88131—28no—
152C4×Dic26—28no—
153C4×Dic26—28no—
154C13×#107C2314yes—
155C13×#106C2314yes—
156C13×#102C2314yes—
157C13×#102C2314yes—
158C13×C22⋊C8C2314yes—
159#88072C2314yes—
160#88072C2314yes—
161C22⋊#1055C2314yes—
162#88058C2314yes—
163#88057C2314yes—
164#88056C2314yes—
165#88056C2314yes—
166#88055C2314yes—
167#88055C2314yes—
168#88054C2314yes—
169#88054C2314yes—
170#88050C2314yes—
171#88050C2314yes—
172#88048C2314yes—
173#88048C2314yes—
174#88047C2314yes—
175#88047C2314yes—
176C2×#3240—131nomaximal, Sylow
177C24×C13—21no—
178C24×C13C2×D411yescharacteristic
179C2×D4×C13—24no—
180C2×D4×C13—21no—
181C2×D4×C13—22no—
182C2×D4×C13—22no—
183C2×D4×C13—44no—
184C2×D4×C13C2412yes—
185C22×C4×C13—22no—
186C22×C4×C13—22no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D412yes—
192C22×C4×C13C2412yes—
193C22×C4×C13C2411yescharacteristic
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—24no—
199C22×Dic13—42no—
200C22×Dic13—42no—
201C22×Dic13—44no—
202C22×Dic13C2×D411yescharacteristic
203C22×Dic13C2×D411yescharacteristic
204C22×Dic13C2×D411yescharacteristic
205C22×Dic13C2×D411yescharacteristic
206C22×Dic13C2×D414yes—
207C22×Dic13C2×D414yes—
208C2×Dic26—22no—
209C2×Dic26—22no—
210C2×Dic26—21no—
211C2×Dic26—24no—
212C2×Dic26—24no—
213C2×Dic26—44no—
214C2×Dic26—44no—
215C2×Dic26C2412yes—
216C2×C8×C13—22no—
217C2×C8×C13—22no—
218C2×C8×C13C2412yes—
219C2×C8×C13C2412yes—
220C13×C4⋊C4—21no—
221C13×C4⋊C4—21no—
222C13×C4⋊C4—21no—
223C13×C4⋊C4C2412yes—
224C13×C4⋊C4C2412yes—
225C13×C4⋊C4C2412yes—
226C13×C22⋊C4—24no—
227C13×C22⋊C4—24no—
228C42×C13—24no—
229C22⋊Dic13—24no—
230C22⋊Dic13—24no—
231C22⋊Dic13—24no—
232C22⋊Dic13—24no—
233C22⋊Dic13—24no—
234C4⋊Dic13—21no—
235C4⋊Dic13—21no—
236C4⋊Dic13—21no—
237C4⋊Dic13—24no—
238C4⋊Dic13—24no—
239C4⋊Dic13—24no—
240C4⋊Dic13C2412yes—
241C4⋊Dic13C2412yes—
242C4⋊Dic13C2412yes—
243#6101—24no—
244#6101—24no—
245#6101—24no—
246#6101—24no—
247#6101—24no—
248#6101—24no—
249#6101—24no—
250C4×Dic13—24no—
251C4×Dic13—24no—
252C4×Dic13C2×D414yes—
253C4×Dic13C2×D414yes—
254C4×Dic13C2×D412yes—
255C4×Dic13C2×D412yes—
256C4×Dic13C2412yes—
257C4×Dic13C2412yes—
258C2×#1055—22no—
259C2×#1055—22no—
260C2×#1055C2412yes—
261C2×#1055C2412yes—
262C2×#533—131no—
263C2×#529—131no—
264#3240—1316no—
265C2×#501—131no—
266C2×#501—131no—
267C2×#489—131no—
268C2×#489—131no—
269C2×#485—131no—
270C2×#485—131no—
271C2×#482—131no—
272C2×#482D1311yescharacteristic
273C2×#479—131no—
274C2×#479—131no—
275C2×#478—131no—
276C2×#478—131no—
277C2×#432—131no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—42no—
283C23×C13—42no—
284C23×C13—42no—
285C23×C13C22×D412yes—
286C23×C13C22×D411yescharacteristic
287D4×C13—22no—
288D4×C13—22no—
289D4×C13—48no—
290D4×C13—42no—
291C2×C4×C13—22no—
292C2×C4×C13—24no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13C22×D412yes—
302C2×C4×C13C22×D411yescharacteristic
303C2×C4×C132−1+412yes—
304C2×C4×C132−1+412yes—
305C2×C4×C13C2511yescharacteristic
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—44no—
315C2×Dic13—44no—
316C2×Dic13—48no—
317C2×Dic13—42no—
318C2×Dic13—42no—
319C2×Dic13—42no—
320C2×Dic13—42no—
321C2×Dic13C22×D412yes—
322C2×Dic13C22×D412yes—
323C2×Dic13C22×D412yes—
324C2×Dic13C22×D412yes—
325Dic26—22no—
326Dic26—22no—
327Dic26—48no—
328Dic26—48no—
329Dic26—42no—
330C8×C13—22no—
331C8×C13—22no—
332#1055—22no—
333#1055—22no—
334#533—138no—
335#533—264no—
336C2×C4⋊Q8—131no—
337C2×C4⋊Q8—131no—
338#529—138no—
339#529—264no—
340C2×#126—261no—
341C2×#125—131no—
342C2×#125—131no—
343C2×#125—131no—
344C2×#124—131no—
345C2×#123—261no—
346C2×C22⋊Q8—131no—
347C2×C22⋊Q8—261no—
348C2×C22⋊Q8—261no—
349C2×#121C2×D1311yescharacteristic
350C2×C4×Q8—131no—
351C2×C4×Q8—261no—
352C2×C4×Q8—261no—
353C2×C4×D4—131no—
354C2×C4×D4—261no—
355C2×#117—131no—
356C2×#117—261no—
357C2×#117C2×D1311yescharacteristic
358C22×C42—131no—
359#501—138no—
360#501—138no—
361#489—138no—
362#489—138no—
363#485—138no—
364#485—138no—
365#482—138no—
366#482C2×D1318yes—
367#479—138no—
368#479—138no—
369#478—138no—
370#478—138no—
371#432—138no—
372C2×#107—131no—
373C2×#107—131no—
374C2×#107—131no—
375C2×#107C2×D1311yescharacteristic
376C2×#106—131no—
377C2×#106—131no—
378C2×#106—131no—
379C2×#106C2×D1311yescharacteristic
380C2×C4⋊C8—131no—
381C2×C4⋊C8—131no—
382C2×#103—131no—
383C2×#103—131no—
384C2×#103—131no—
385C2×#103—131no—
386C2×#102—131no—
387C2×#102—131no—
388C2×#102C2×D1311yescharacteristic
389C2×#102C2×D1311yescharacteristic
390C2×C22⋊C8—131no—
391C2×C22⋊C8C2×D1311yescharacteristic
392C2×#97—131no—
393C2×#97—131no—
394C22×C13—22no—
395C22×C13—22no—
396C22×C13—22no—
397C22×C13—44no—
398C22×C13—42no—
399C22×C13—42no—
400C22×C13—42no—
401C22×C13—84no—
402C22×C13#53612yes—
403C22×C13#57512yes—
404C22×C13#57512yes—
405C22×C13C23×D411yescharacteristic
406C4×C13—22no—
407C4×C13—42no—
408C4×C13—42no—
409C4×C13—42no—
410C4×C13#53612yes—
411C4×C13C2×2−1+411yescharacteristic
412C4×C13C2×2−1+411yescharacteristic
413Dic13—22no—
414Dic13—22no—
415Dic13—22no—
416Dic13—22no—
417Dic13—42no—
418Dic13—42no—
419Dic13—42no—
420Dic13—42no—
421C22×Q8—131no—
422C22×Q8—261no—
423C22×Q8—261no—
424C22×D4—21no—
425C22×D4C22×D1311yescharacteristic
426C23×C4—131no—
427C23×C4—131no—
428C23×C4—261no—
429C23×C4C22×D1311yescharacteristic
430C22×C8—131no—
431C22×C8—131no—
432C22×C8C22×D1311yescharacteristic
433C22×C8C22×D1311yescharacteristic
434C4⋊Q8—134no—
435C4⋊Q8—134no—
436C4⋊Q8—262no—
437C4⋊Q8—262no—
438#126—268no—
439#125—134no—
440#125—134no—
441#125—134no—
442#125—262no—
443#125—262no—
444#125—262no—
445#124—134no—
446#124—262no—
447#123—268no—
448C22⋊Q8—134no—
449C22⋊Q8—268no—
450C22⋊Q8—268no—
451C22⋊Q8—262no—
452#121—22no—
453#121C22×D1314yes—
454C4×Q8—134no—
455C4×Q8—268no—
456C4×Q8—268no—
457C4×Q8—262no—
458C4×D4—134no—
459C4×D4—262no—
460C4×D4—268no—
461#117—22no—
462#117—134no—
463#117—268no—
464#117—262no—
465#117C22×D1314yes—
466C2×C4⋊C4—131no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—261no—
470C2×C4⋊C4—261no—
471C2×C4⋊C4—261no—
472C2×C4⋊C4—261no—
473C2×C4⋊C4—261no—
474C2×C4⋊C4—261no—
475C2×C4⋊C4—261no—
476C2×C4⋊C4—261no—
477C2×C4⋊C4—261no—
478C2×C4⋊C4—261no—
479C2×C4⋊C4C22×D1311yescharacteristic
480C2×C4⋊C4C22×D1311yescharacteristic
481C2×C4⋊C4C22×D1311yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—261no—
485C2×C22⋊C4—261no—
486C2×C22⋊C4—261no—
487C2×C22⋊C4—261no—
488C2×C22⋊C4—261no—
489C2×C42—21no—
490C2×C42—131no—
491C2×C42—131no—
492C2×C42—134no—
493C2×C42—131no—
494C2×C42—131no—
495C2×C42—134no—
496C2×C42—261no—
497C2×C42—261no—
498#107—134no—
499#107—134no—
500#107—134no—
501#107C22×D1314yes—
502#106—134no—
503#106—134no—
504#106—134no—
505#106C22×D1314yes—
506C4⋊C8—134no—
507C4⋊C8—134no—
508#103—134no—
509#103—134no—
510#103—134no—
511#103—134no—
512#102—134no—
513#102—134no—
514#102C22×D1314yes—
515#102C22×D1314yes—
516C22⋊C8—134no—
517C22⋊C8C22×D1314yes—
518#97—134no—
519#97—134no—
520C2×C13—42no—
521C2×C13—82no—
522C2×C13#324014yescomplemented
523C2×C13C2×#53611yescharacteristic
524C2×C13C2×#57511yescharacteristic
525C2×C13C2×#57511yescharacteristic
526C24—21no—
527C24D4×D1311yescharacteristic
528C2×Q8—132no—
529C2×Q8—264no—
530C2×Q8—264no—
531C2×Q8—261no—
532C2×Q8—262no—
533C2×Q8—262no—
534C2×Q8—524no—
535C2×Q8—524no—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—44no—
541C2×D4C23×D1312yes—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—131no—
548C22×C4—131no—
549C22×C4—131no—
550C22×C4—131no—
551C22×C4—134no—
552C22×C4—134no—
553C22×C4—264no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—261no—
558C22×C4—522no—
559C22×C4—522no—
560C22×C4—524no—
561C22×C4D4×D1312yes—
562C22×C4D4×D1311yescharacteristic
563C22×C4C23×D1312yes—
564C22×C4C23×D1311yescharacteristic
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—132no—
568C2×C8—132no—
569C2×C8—262no—
570C2×C8—262no—
571C2×C8C23×D1312yes—
572C2×C8C23×D1312yes—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—132no—
577C4⋊C4—132no—
578C4⋊C4—132no—
579C4⋊C4—264no—
580C4⋊C4—264no—
581C4⋊C4—264no—
582C4⋊C4—264no—
583C4⋊C4—264no—
584C4⋊C4—264no—
585C4⋊C4—264no—
586C4⋊C4—264no—
587C4⋊C4—264no—
588C4⋊C4—261no—
589C4⋊C4—261no—
590C4⋊C4—261no—
591C4⋊C4—264no—
592C4⋊C4C23×D1312yes—
593C4⋊C4C23×D1312yes—
594C4⋊C4C23×D1312yes—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—264no—
598C22⋊C4—264no—
599C22⋊C4—264no—
600C22⋊C4—264no—
601C22⋊C4—264no—
602C42—24no—
603C42—134no—
604C42—132no—
605C42—134no—
606C42—132no—
607C42—132no—
608C42—132no—
609C42—264no—
610C42—264no—
611C13C2×#324011yescharacteristic, complemented, Sylow
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23C2×D4×D1312yes—
620C23C2×D4×D1311yescharacteristic
621Q8—262no—
622Q8—262no—
623Q8—528no—
624Q8—528no—
625Q8—522no—
626D4—22no—
627D4—22no—
628D4—48no—
629D4—42no—
630C2×C4—22no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—132no—
641C2×C4—132no—
642C2×C4—132no—
643C2×C4—132no—
644C2×C4—262no—
645C2×C4—262no—
646C2×C4—262no—
647C2×C4—262no—
648C2×C4—262no—
649C2×C4—262no—
650C2×C4—262no—
651C2×C4—262no—
652C2×C4—524no—
653C2×C4—524no—
654C2×C4—528no—
655C2×C4—522no—
656C2×C4—522no—
657C2×C4—522no—
658C2×C4—522no—
659C2×C4C2×D4×D1312yes—
660C2×C4C2×D4×D1311yescharacteristic
661C2×C4#8825712yes—
662C2×C4#8825712yes—
663C2×C4C24×D1311yescharacteristic
664C8—22no—
665C8—22no—
666C8—262no—
667C8—262no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—84no—
676C22#1171935312yes—
677C22#1171947312yes—
678C22#1171947812yes—
679C22C22×D4×D1311yescharacteristic
680C4—22no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—262no—
685C4—262no—
686C4—262no—
687C4—262no—
688C4—522no—
689C4—522no—
690C4—522no—
691C4—522no—
692C4#1171935312yes—
693C4C2×#8825711yescharacteristic
694C4C2×#8825711yescharacteristic
695C2—42no—
696C2—82no—
697C2#1312607414yesdirect product factor
698C2C2×#1171935311yescharacteristic
699C2C2×#1171947811yescharacteristic
700C2C2×#1171947311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#482C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenterC2×#482D13
hypocenterC13C2×#3240
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#11719222C2semidirect
3. #13126074C2direct (N × H)
4. C2×#11718537C2semidirect
5. C2×#11718517C2semidirect
6. C2×#11718426C2semidirect
7. C2×#11718426C2semidirect
8. C2×#11718384C2semidirect
9. C2×#11718657C2semidirect
11. C2×#11718518C2semidirect
12. C2×#11718538C2semidirect
13. C2×#11718424C2semidirect
14. C2×#11718427C2semidirect
15. C2×#11718380C2semidirect
29. #11719222C22semidirect
60. #11718657C22semidirect
67. #11718538C22semidirect
68. #11718537C22semidirect
69. #11718518C22semidirect
70. #11718517C22semidirect
71. #11718427C22semidirect
72. #11718426C22semidirect
73. #11718426C22semidirect
74. #11718424C22semidirect
75. #11718384C22semidirect
76. #11718380C22semidirect
522. C2×C13#3240semidirect
611. C13C2×#3240semidirect
697. C2#13126074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192222
C2×#117193052
#131260742
C2×#117185372
C2×#117185172
C2×#117184262
C2×#117183842
C2×#117186572
C2×#117186962
C2×#117185182
C2×#117185382
C2×#117184242
C2×#117184272
C2×#117183802
C2×C13×#4822
C2×#324013