Finite Group Databasebeta

← #15901419

Subgroups — #15901419

Order 3328.

992 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718705C211yesmaximal, characteristic, complemented
2C2×#11718893C211yesmaximal, characteristic
3#13117703C211yesmaximal, characteristic, complemented
4#13116231C211yesmaximal, characteristic, complemented
5#13116224C211yesmaximal, characteristic, complemented
6#13116079C211yesmaximal, characteristic, complemented
7#13116072C211yesmaximal, characteristic, complemented
8#13115769C211yesmaximal, characteristic, complemented
9#13115760C211yesmaximal, characteristic, complemented
10#13115474C211yesmaximal, characteristic, complemented
11#13115453C211yesmaximal, characteristic, complemented
12#13115270C211yesmaximal, characteristic, complemented
13#13115021C211yesmaximal, characteristic, complemented
14#13114776C211yesmaximal, characteristic
15C13×#2432C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C2×C13×C4⋊Q8C2211yescharacteristic
18C2×C13×#124C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C2×#88131—21no—
23C13×#394—21no—
24C13×#394—21no—
25C13×#391C2211yescharacteristic
26C13×#390C2211yescharacteristic
27C13×#385—21no—
28C13×#385—21no—
29C4×C13×C22⋊C4C2211yescharacteristic
30#11718893—24no—
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39C2×#88072C2211yescharacteristic
40C2×#88072C2211yescharacteristic
41C2×#88072C2211yescharacteristic
42C2×#88072C2211yescharacteristic
43#11718873C2211yescharacteristic
44C2×C22⋊#1055C2211yescharacteristic
45#11718705—24no—
46C2×#88047C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48#11718604—21no—
49C4×C4⋊Dic13C2211yescharacteristic
50C4×C4⋊Dic13C2211yescharacteristic
51#11718589C2211yescharacteristic
52#11718589C2211yescharacteristic
53C2×C4⋊#1055C2211yescharacteristic
54C2×C4⋊#1055C2211yescharacteristic
55#11718314—21no—
56#11718314—21no—
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C2×C13×#41—22no—
62C2×C13×#41—22no—
63C2×C13×#41—22no—
64C2×C13×#41—22no—
65C2×C13×#41—41no—
66C2×C13×#41—41no—
67C22×Q8×C13C2311yescharacteristic
68C22×Q8×C13C2311yescharacteristic
69C22×D4×C13—21no—
70C22×D4×C13C2311yescharacteristic
71C23×C4×C13—21no—
72C23×C4×C13C2311yescharacteristic
73C23×Dic13—21no—
74C13×C4⋊Q8—22no—
75C13×C4⋊Q8—41no—
76C13×#124—22no—
77C13×#124—41no—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8—22no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4D411yescharacteristic
90C2×C13×C22⋊C4D411yescharacteristic
91C2×C42×C13C2311yescharacteristic
92C2×C42×C13C2311yescharacteristic
93C2×C22⋊Dic13—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13D414yes—
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×#6101—21no—
102C2×#6101—21no—
103C2×C4×Dic13—21no—
104C2×C4×Dic13—21no—
105C2×#6099—22no—
106C2×#6099—41no—
107C2×#6099—41no—
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112#88131—44no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95D411yescharacteristic
116C13×#95D411yescharacteristic
117#88075—22no—
118#88075—22no—
119#88075—22no—
120#88075—22no—
121#88075—22no—
122#88075—41no—
123#88075—41no—
124#88075—41no—
125#88072—22no—
126#88072—22no—
127#88072—22no—
128#88072—41no—
129#88071—21no—
130#88071—21no—
131#88071—21no—
132#88071—21no—
133#88071—21no—
134C22⋊#1055—22no—
135#88047—22no—
136#88047—22no—
137C4⋊#1055—41no—
138C4⋊#1055—41no—
139#24489—131nomaximal, Sylow
140C24×C13—21no—
141C24×C13C2×D411yescharacteristic
142C13×#41—28no—
143C13×#41—44no—
144C13×#41—44no—
145C13×#41—44no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13—21no—
151C2×Q8×C13—21no—
152C2×Q8×C13—21no—
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13#4112yes—
158C2×D4×C13—21no—
159C2×D4×C13—21no—
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13—21no—
163C2×D4×C13—42no—
164C2×D4×C13—42no—
165C2×D4×C13—42no—
166C2×D4×C13#4112yes—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—42no—
175C22×C4×C13—42no—
176C22×C4×C13—42no—
177C22×C4×C13C2×D412yes—
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13#4112yes—
184C22×C4×C13C2411yescharacteristic
185C22×Dic13—24no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—42no—
191C22×Dic13—42no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—42no—
195C13×C4⋊C4—42no—
196C13×C4⋊C4—42no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—41no—
199C13×C22⋊C4—42no—
200C13×C22⋊C4—42no—
201C13×C22⋊C4—42no—
202C13×C22⋊C4—42no—
203C13×C22⋊C4—42no—
204C42×C13—21no—
205C42×C13—21no—
206C42×C13—21no—
207C42×C13—21no—
208C22⋊Dic13—42no—
209C4⋊Dic13—24no—
210C4⋊Dic13—21no—
211C4⋊Dic13—21no—
212C4⋊Dic13—21no—
213C4⋊Dic13—21no—
214C4⋊Dic13—21no—
215C4⋊Dic13—21no—
216C4⋊Dic13C2×D412yes—
217C4⋊Dic13C2×D412yes—
218#6101—42no—
219#6101—42no—
220C4×Dic13—42no—
221C4×Dic13—42no—
222#6099—44no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#484—131no—
236C2×#417—131no—
237#2432D1311yescharacteristic
238#2344—131no—
239#2068—131no—
240#2067—131no—
241#2043—131no—
242#2042—131no—
243#1983—131no—
244#1981—131no—
245#1928—131no—
246#1925—131no—
247#1894—131no—
248#1851—131no—
249#1788—131no—
250C23×C13—21no—
251C23×C13—21no—
252C23×C13—21no—
253C23×C13—21no—
254C23×C13—21no—
255C23×C13—21no—
256C23×C13—22no—
257C23×C13—41no—
258C23×C13—41no—
259C23×C13—41no—
260C23×C13—41no—
261C23×C13—41no—
262C23×C13—41no—
263C23×C13#12112yes—
264C23×C13C22×D411yescharacteristic
265Q8×C13—22no—
266Q8×C13—22no—
267Q8×C13—41no—
268Q8×C13—41no—
269Q8×C13—41no—
270Q8×C13—41no—
271Q8×C13—41no—
272Q8×C13—41no—
273D4×C13—22no—
274D4×C13—22no—
275D4×C13—48no—
276D4×C13—41no—
277D4×C13—41no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—22no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—48no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13#12112yes—
306C2×C4×C13AGL(1,ℤ/8)12yes—
307C2×C4×C13C22×D411yescharacteristic
308C2×C4×C13C2×#4111yescharacteristic
309C2×C4×C13C2×#4111yescharacteristic
310C2×C4×C13C2×#4111yescharacteristic
311C2×C4×C13H(5,𝔽2)11yescharacteristic
312C2×C4×C13H(5,𝔽2)11yescharacteristic
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—48no—
316C2×Dic13—41no—
317C2×Dic13—41no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326#1055—41no—
327#1055—41no—
328#1055—41no—
329#1055—41no—
330C22×#41C2×D1311yescharacteristic
331C22×M16—131no—
332C2×C4⋊Q8C2×D1311yescharacteristic
333C2×#124C2×D1311yescharacteristic
334C2×C22⋊Q8C2×D1311yescharacteristic
335C2×#117—261no—
336C22×C4⋊C4—131no—
337#484—264no—
338C2×#107—131no—
339C2×#107—131no—
340C2×C4⋊C8—131no—
341C2×C4⋊C8—131no—
342#417—264no—
343C2×#103—131no—
344C2×#103—131no—
345C2×#103—131no—
346C2×#103—131no—
347C2×#103—131no—
348C2×#103—131no—
349C2×#103—131no—
350C2×#103—131no—
351C2×#102—131no—
352C2×#102—131no—
353C2×#102—131no—
354C2×#102—131no—
355C2×C22⋊C8—131no—
356#394—21no—
357#394—21no—
358#391C2×D1311yescharacteristic
359#390C2×D1311yescharacteristic
360#389—131no—
361#389—131no—
362#387—261no—
363#387—261no—
364#385—21no—
365#385—21no—
366#381—261no—
367#380—131no—
368C4×C4⋊C4—131no—
369C4×C4⋊C4—131no—
370C4×C22⋊C4C2×D1311yescharacteristic
371#340—131no—
372#340—131no—
373#336—131no—
374#336—131no—
375C22×C13—22no—
376C22×C13—22no—
377C22×C13—22no—
378C22×C13—41no—
379C22×C13—41no—
380C22×C13—41no—
381C22×C13—41no—
382C22×C13—42no—
383C22×C13—42no—
384C22×C13—42no—
385C22×C13—81no—
386C22×C13—81no—
387C22×C13—81no—
388C22×C13—81no—
389C22×C13C2×#12111yescharacteristic
390C22×C13#54611yescharacteristic
391C22×C13#54611yescharacteristic
392C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C13#57511yescharacteristic
394C22×C13#57811yescharacteristic
395C22×C13#57811yescharacteristic
396C4×C13—22no—
397C4×C13—22no—
398C4×C13—41no—
399C4×C13—42no—
400C4×C13—41no—
401C4×C13—41no—
402C4×C13—81no—
403C4×C13—81no—
404C4×C13#52511yescharacteristic
405C4×C13#53511yescharacteristic
406C4×C13#55111yescharacteristic
407C4×C13#55111yescharacteristic
408Dic13—42no—
409Dic13—42no—
410Dic13—81no—
411Dic13—81no—
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—22no—
416C2×#41—41no—
417C2×#41—41no—
418C22×Q8C22×D1311yescharacteristic
419C22×Q8C22×D1311yescharacteristic
420C22×D4—21no—
421C22×D4C22×D1311yescharacteristic
422C23×C4—21no—
423C23×C4—261no—
424C23×C4C22×D1311yescharacteristic
425C2×M16—262no—
426C2×M16—521no—
427C2×M16—521no—
428C22×C8—131no—
429C22×C8—131no—
430C22×C8—131no—
431C22×C8—131no—
432C4⋊Q8—22no—
433C4⋊Q8—41no—
434#124—22no—
435#124—41no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438#117—524no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—134no—
443C2×C4⋊C4—131no—
444C2×C4⋊C4—131no—
445C2×C4⋊C4—131no—
446C2×C4⋊C4—131no—
447C2×C4⋊C4—262no—
448C2×C4⋊C4—261no—
449C2×C4⋊C4—261no—
450C2×C4⋊C4—261no—
451C2×C4⋊C4C22×D1311yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—261no—
458C2×C22⋊C4C22⋊D1311yescharacteristic
459C2×C22⋊C4C22⋊D1311yescharacteristic
460C2×C42—261no—
461C2×C42—261no—
462C2×C42C22×D1311yescharacteristic
463C2×C42C22×D1311yescharacteristic
464#107—262no—
465#107—262no—
466C4⋊C8—521no—
467C4⋊C8—521no—
468#103—262no—
469#103—262no—
470#103—262no—
471#103—262no—
472#103—262no—
473#103—521no—
474#103—521no—
475#103—521no—
476#102—262no—
477#102—262no—
478#102—262no—
479#102—521no—
480C22⋊C8—262no—
481#95—21no—
482#95—21no—
483#95—261no—
484#95—261no—
485#95—261no—
486#95—261no—
487#95—261no—
488#95C22⋊D1311yescharacteristic
489#95C22⋊D1311yescharacteristic
490C2×C13—42no—
491C2×C13—82no—
492C2×C13#241111yescharacteristic
493C2×C13#303611yescharacteristic
494C2×C13#304411yescharacteristic
495C2×C13#330811yescharacteristic
496C2×C13#331511yescharacteristic
497C2×C13#332711yescharacteristic
498C2×C13#333011yescharacteristic
499C24—21no—
500C24C2×C22⋊D1311yescharacteristic
501#41—28no—
502#41—44no—
503#41—44no—
504#41—44no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8#612912yes—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4#612912yes—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—264no—
537C22×C4—261no—
538C22×C4—261no—
539C22×C4—261no—
540C22×C4—261no—
541C22×C4—522no—
542C22×C4—522no—
543C22×C4D4×D1312yes—
544C22×C4#612912yes—
545C22×C4C2×C22⋊D1311yescharacteristic
546C22×C4C2×C22⋊D1311yescharacteristic
547C22×C4C2×C22⋊D1311yescharacteristic
548C22×C4C2×C22⋊D1311yescharacteristic
549C22×C4C2×C22⋊D1311yescharacteristic
550C22×C4C23×D1311yescharacteristic
551M16—524no—
552C2×C8—261no—
553C2×C8—261no—
554C2×C8—261no—
555C2×C8—261no—
556C2×C8—261no—
557C2×C8—261no—
558C2×C8—261no—
559C2×C8—261no—
560C2×C8—261no—
561C2×C8—261no—
562C2×C8—261no—
563C2×C8—261no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—132no—
570C4⋊C4—132no—
571C4⋊C4—264no—
572C4⋊C4—261no—
573C4⋊C4—261no—
574C4⋊C4—261no—
575C4⋊C4—261no—
576C4⋊C4—261no—
577C4⋊C4—261no—
578C4⋊C4—522no—
579C4⋊C4—522no—
580C22⋊C4—22no—
581C22⋊C4—41no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—522no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—522no—
593C42—522no—
594C13#2448911yescharacteristic, complemented, Sylow
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—22no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23#8819212yes—
609C23C22×C22⋊D1311yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618D4—22no—
619D4—22no—
620D4—48no—
621D4—41no—
622D4—41no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—48no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—262no—
651C2×C4—262no—
652C2×C4—528no—
653C2×C4—521no—
654C2×C4—521no—
655C2×C4—521no—
656C2×C4—521no—
657C2×C4—521no—
658C2×C4—521no—
659C2×C4—521no—
660C2×C4—521no—
661C2×C4—521no—
662C2×C4—521no—
663C2×C4#8819212yes—
664C2×C4#8820312yes—
665C2×C4C2×D4×D1311yescharacteristic
666C2×C4C2×#612911yescharacteristic
667C2×C4C2×#612911yescharacteristic
668C2×C4C2×#612911yescharacteristic
669C2×C4#8825111yescharacteristic
670C2×C4#8825111yescharacteristic
671C8—521no—
672C8—521no—
673C8—521no—
674C8—521no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×#8819211yescharacteristic
690C22#1171951111yescharacteristic
691C22#1171951111yescharacteristic
692C22C2×#8820311yescharacteristic
693C22#1171952711yescharacteristic
694C22#1171954311yescharacteristic
695C22#1171954311yescharacteristic
696C4—22no—
697C4—22no—
698C4—42no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—81no—
703C4—81no—
704C4—522no—
705C4—522no—
706C4—1041no—
707C4—1041no—
708C4#1171929111yescharacteristic
709C4#1171929211yescharacteristic
710C4#1171929211yescharacteristic
711C4#1171929711yescharacteristic
712C2—42no—
713C2—82no—
714C2#1311821711yescharacteristic
715C2#1312429611yescharacteristic
716C2#1312436211yescharacteristic
717C2#1312682711yescharacteristic
718C2#1312693211yescharacteristic
719C2#1312710411yescharacteristic
720C2#1312714111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2432C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
hypercenter#2432D13
hypocenterC13#24489
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2432

Complements

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

NH ≅ G/Ntype
1. C2×#11718705C2semidirect
3. #13117703C2semidirect
4. #13116231C2semidirect
5. #13116224C2semidirect
6. #13116079C2semidirect
7. #13116072C2semidirect
8. #13115769C2semidirect
9. #13115760C2semidirect
10. #13115474C2semidirect
11. #13115453C2semidirect
12. #13115270C2semidirect
13. #13115021C2semidirect
594. C13#24489semidirect

Maximal subgroups

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

subgroupindex
C2×#117187052
C2×#117188932
#131177032
#131162312
#131162242
#131160792
#131160722
#131157692
#131157602
#131154742
#131154532
#131152702
#131150212
#131147762
C13×#24322
#2448913