Subgroups — #28383404

Order 14272.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20297244	C₂	1	1	yes	maximal, characteristic
2	#20297236	C₂	1	1	yes	maximal, characteristic
3	#108×C₂₂₃	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₂₂₃	—	2	1	no	—
5	C₂₂₃⋊C₁₆	C₄	1	2	yes	complemented
6	M₁₆×C₂₂₃	—	2	1	no	—
7	C₂×C₈×C₂₂₃	C₂²	1	1	yes	characteristic
8	C₂×Dic₂₂₃	—	4	1	no	—
9	C₂×C₄×C₂₂₃	D₄	1	1	yes	characteristic
10	C₈×C₂₂₃	—	4	1	no	—
11	C₈×C₂₂₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₂₃	Q₈	1	1	yes	characteristic
13	C₂²×C₂₂₃	SD₁₆	1	1	yes	characteristic
14	C₄×C₂₂₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₂₂₃	SD₁₆	1	1	yes	characteristic
16	Dic₂₂₃	—	8	1	no	—
17	C₂×C₂₂₃	—	2	1	no	—
18	C₂×C₂₂₃	#106	1	1	yes	characteristic
19	C₂₂₃	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	223	1	no	maximal, Sylow
21	M₃₂	—	223	1	no	—
22	#108	D₂₂₃	1	1	yes	characteristic
23	#106	—	223	1	no	—
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂×D₂₂₃	1	1	yes	characteristic
26	C₄⋊C₄	—	446	1	no	—
27	C₁₆	—	223	2	no	—
28	C₂×C₄	—	892	1	no	—
29	C₂×C₄	C₂²⋊D₂₂₃	1	1	yes	characteristic
30	C₈	—	4	1	no	—
31	C₈	C₄×D₂₂₃	1	1	yes	characteristic
32	C₈	Dic₄₄₆	1	1	yes	characteristic
33	C₂²	#16813157	1	1	yes	characteristic
34	C₄	—	1784	1	no	—
35	C₄	Dic₂₂₃⋊C₄	1	1	yes	characteristic
36	C₄	#16813158	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#20297235	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₂₂₃⋊C₁₆	C₄	semidirect
19. C₂₂₃	#365	semidirect

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