Subgroups — #13092243

Order 1472.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10625000	C₂	1	2	yes	maximal
3	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
4	C₄⋊Dic₂₃	—	2	2	no	—
5	C₁₆×C₂₃	C₄	1	2	yes	complemented
6	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
7	C₂×Dic₂₃	—	4	2	no	—
8	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₃	Q₈	1	1	yes	characteristic
10	C₂²×C₂₃	D₈	1	1	yes	characteristic
11	C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₂₃	Q₁₆	1	1	yes	characteristic
13	Dic₂₃	—	8	2	no	—
14	#366	—	23	1	no	maximal, Sylow
15	C₂×C₂₃	#107	1	1	yes	characteristic
16	C₂×C₂₃	D₁₆	1	1	yes	characteristic
17	C₂×C₂₃	Q₃₂	1	1	yes	characteristic
18	C₂×C₁₆	D₂₃	1	1	yes	characteristic
19	#107	—	23	2	no	—
20	C₂₃	#366	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
22	C₄⋊C₄	—	46	2	no	—
23	C₁₆	Dic₂₃	1	2	yes	complemented
24	C₂×C₄	—	92	2	no	—
25	C₂×C₄	D₉₂	1	1	yes	characteristic
26	C₈	Dic₄₆	1	1	yes	characteristic
27	C₈	C₂×Dic₂₃	1	1	yes	characteristic
28	C₂²	D₁₈₄	1	1	yes	characteristic
29	C₄	—	184	2	no	—
30	C₄	Dic₉₂	1	1	yes	characteristic
31	C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
32	C₂	D₃₆₈	1	1	yes	characteristic
33	C₂	Dic₁₈₄	1	1	yes	characteristic
34	C₂	#10625000	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.