Subgroups — #28412373

Order 14656.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20301062	C₂	1	2	yes	maximal
2	#20300899	C₂	1	1	yes	maximal, characteristic
3	#16814669	C₄	1	4	yes	complemented
4	C₂×#14270080	C₄	1	1	yes	characteristic
5	C₂×#14270080	C₂²	1	1	yes	characteristic
6	C₄²×C₂₂₉	C₄	1	1	yes	characteristic
7	#14270080	—	2	1	no	—
8	#14270080	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₂₂₉	—	2	1	no	—
10	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₂₂₉	M₁₆	1	1	yes	characteristic
12	C₄×C₂₂₉	—	4	1	no	—
13	C₄×C₂₂₉	C₄²	1	1	yes	characteristic
14	C₄×C₂₂₉	M₁₆	1	1	yes	characteristic
15	C₂×C₂₂₉	—	2	1	no	—
16	C₂×C₂₂₉	#97	1	1	yes	characteristic
17	C₂₂₉	#347	1	1	yes	characteristic, complemented, Sylow
18	#347	—	229	1	no	maximal, Sylow
19	M₃₂	—	229	2	no	—
20	#97	—	229	1	no	—
21	C₂×C₈	—	229	1	no	—
22	C₂×C₈	—	229	1	no	—
23	C₄²	#11745021	1	1	yes	characteristic
24	C₁₆	—	229	4	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
27	C₈	—	458	1	no	—
28	C₈	—	229	2	no	—
29	C₂²	#16814675	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	C₄×#11745021	1	1	yes	characteristic
32	C₄	#16814676	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#20301043	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #16814669	C₄	semidirect
17. C₂₂₉	#347	semidirect

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