Subgroups — #36378648

Order 22592.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#15667732	C₂	1	2	yes	maximal
2	C₈×Dic₃₅₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#15667732	—	2	2	no	—
4	C₂×#15667725	C₄	1	1	yes	characteristic
5	C₄×Dic₃₅₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₅₃	C₄	1	1	yes	characteristic
7	#15667732	—	4	2	no	—
8	C₂×Dic₃₅₃	D₄	1	1	yes	characteristic
9	C₂×Dic₃₅₃	Q₈	1	1	yes	characteristic
10	#15667725	—	2	1	no	—
11	C₂×C₄×C₃₅₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₅₃	C₈	1	2	yes	complemented
13	C₂²×C₃₅₃	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₃₅₃	C₂×C₈	1	1	yes	characteristic
15	C₄×C₃₅₃	M₁₆	1	1	yes	characteristic
16	Dic₃₅₃	—	2	1	no	—
17	Dic₃₅₃	SD₁₆	1	2	yes	—
18	C₂×C₃₅₃	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₃₅₃	#106	1	1	yes	characteristic
20	C₂×C₃₅₃	#108	1	1	yes	characteristic
21	C₃₅₃	#334	1	1	yes	characteristic, complemented, Sylow
22	#334	—	353	1	no	maximal, Sylow
23	C₄⋊C₈	—	353	2	no	—
24	C₄×C₈	—	353	1	no	—
25	C₂×C₈	—	353	1	no	—
26	C₂×C₈	—	706	2	no	—
27	C₂×C₈	#13083443	1	1	yes	characteristic
28	C₄²	—	353	1	no	—
29	C₂×C₄	—	353	1	no	—
30	C₂×C₄	—	353	1	no	—
31	C₂×C₄	C₂×#13083443	1	1	yes	characteristic
32	C₈	—	1412	2	no	—
33	C₈	—	706	1	no	—
34	C₈	#15667732	1	2	yes	complemented
35	C₂²	C₄⋊#13083443	1	1	yes	characteristic
36	C₄	—	353	2	no	—
37	C₄	—	706	1	no	—
38	C₄	C₂×#15667732	1	1	yes	characteristic
39	C₄	#19150747	1	1	yes	characteristic
40	C₂	C₄⋊#15667732	1	1	yes	characteristic
41	C₂	#26015060	1	1	yes	characteristic
42	C₂	#26015062	1	1	yes	characteristic

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

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