Subgroups — #20297296

Order 7136.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Dic₂₂₃	C₂	1	2	yes	maximal
2	Dic₂₂₃⋊C₄	C₂	1	4	yes	maximal
3	C₄²×C₂₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₂₃	C₂²	1	4	yes	—
5	C₂×C₄×C₂₂₃	C₂²	1	2	yes	—
6	C₂×C₄×C₂₂₃	C₂²	1	1	yes	characteristic
7	C₂²×C₂₂₃	C₂³	1	1	yes	characteristic
8	C₄×C₂₂₃	—	2	2	no	—
9	C₄×C₂₂₃	Q₈	1	2	yes	—
10	Dic₂₂₃	—	2	4	no	—
11	C₂×C₂₂₃	C₂×Q₈	1	1	yes	characteristic
12	C₂×C₂₂₃	#41	1	2	yes	—
13	C₂₂₃	#125	1	1	yes	characteristic, complemented, Sylow
14	#125	—	223	1	no	maximal, Sylow
15	C₄⋊C₄	—	223	4	no	—
16	C₄⋊C₄	—	223	2	no	—
17	C₄²	D₂₂₃	1	1	yes	characteristic
18	C₂×C₄	—	223	4	no	—
19	C₂×C₄	C₂×D₂₂₃	1	2	yes	—
20	C₂×C₄	C₂×D₂₂₃	1	1	yes	characteristic
21	C₂²	C₂²×D₂₂₃	1	1	yes	characteristic
22	C₄	—	2	2	no	—
23	C₄	—	446	4	no	—
24	C₄	Dic₄₄₆	1	2	yes	—
25	C₂	C₂×Dic₄₄₆	1	1	yes	characteristic
26	C₂	#16813170	1	2	yes	—

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

N	H ≅ G/N	type
13. C₂₂₃	#125	semidirect