Subgroups — #16813719

Order 3616.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14268659	C₂	1	2	yes	maximal, complemented
2	#14268655	C₂	1	1	yes	maximal, characteristic
3	C₄×D₁₁₃	C₄	1	1	yes	characteristic
4	#11744753	C₄	1	1	yes	characteristic
5	#11744753	C₂²	1	1	yes	characteristic
6	C₂×D₁₁₃	C₈	1	1	yes	characteristic
7	C₄×C₁₁₃	C₈	1	1	yes	characteristic
8	Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₁₃	C₂×C₈	1	1	yes	characteristic
10	D₁₁₃	—	2	1	no	—
11	C₁₁₃	M₃₂	1	1	yes	characteristic, complemented, Sylow
12	M₃₂	—	113	1	no	maximal, Sylow
13	C₂×C₈	—	113	1	no	—
14	C₁₆	—	113	2	no	—
15	C₂×C₄	—	113	1	no	—
16	C₈	—	113	1	no	—
17	C₈	—	113	1	no	—
18	C₂²	—	113	1	no	—
19	C₄	—	113	1	no	—
20	C₄	#11744762	1	1	yes	characteristic
21	C₂	—	226	1	no	—
22	C₂	C₂×#11744762	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #14268659	C₂	semidirect
11. C₁₁₃	M₃₂	semidirect

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