Subgroups — #28412369

Order 14656.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16814669	C₂	1	2	yes	maximal
2	C₄×#14270080	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	C₈	1	2	yes	—
8	#14270080	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₂₂₉	C₈	1	2	yes	—
10	C₂×C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₂₂₉	C₂×C₈	1	1	yes	characteristic
12	C₄×C₂₂₉	—	2	2	no	—
13	C₄×C₂₂₉	C₄²	1	1	yes	characteristic
14	C₄×C₂₂₉	C₂×C₈	1	1	yes	characteristic
15	C₂×C₂₂₉	C₄×C₈	1	1	yes	characteristic
16	C₂×C₂₂₉	M₃₂	1	2	yes	—
17	C₂₂₉	#346	1	1	yes	characteristic, complemented, Sylow
18	#346	—	229	1	no	maximal, Sylow
19	C₂×C₁₆	—	229	2	no	—
20	C₄×C₈	—	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	#14270087	1	2	yes	—
26	C₂×C₄	C₂×#11745021	1	1	yes	characteristic
27	C₈	—	229	2	no	—
28	C₈	—	229	2	no	—
29	C₂²	C₂×#14270087	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	C₄×#11745021	1	1	yes	characteristic
32	C₄	D₂₂₉⋊C₈	1	1	yes	characteristic
33	C₂	C₄×#14270087	1	1	yes	characteristic
34	C₂	#20301062	1	2	yes	—

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

N	H ≅ G/N	type
3. #16814669	C₄	semidirect
17. C₂₂₉	#346	semidirect

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