Subgroups — #14272056

Order 1856.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745214	C₂	1	2	yes	maximal
2	#11745163	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×C₂₉	C₄	1	1	yes	characteristic
4	C₄×Dic₂₉	C₄	1	1	yes	characteristic
5	C₂×#6597	C₂²	1	1	yes	characteristic
6	#90770	C₄	1	4	yes	complemented
7	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
8	C₂×Dic₂₉	—	2	1	no	—
9	C₈×C₂₉	—	2	1	no	—
10	#6597	C₂×C₄	1	2	yes	—
11	C₂²×C₂₉	M₁₆	1	1	yes	characteristic
12	C₄×C₂₉	C₄²	1	1	yes	characteristic
13	C₄×C₂₉	M₁₆	1	1	yes	characteristic
14	Dic₂₉	—	4	1	no	—
15	#347	—	29	1	no	maximal, Sylow
16	C₂×C₂₉	—	2	1	no	—
17	C₂×C₂₉	#97	1	1	yes	characteristic
18	M₃₂	—	29	2	no	—
19	#97	—	29	1	no	—
20	C₂₉	#347	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₈	—	29	1	no	—
22	C₂×C₈	#1181	1	1	yes	characteristic
23	C₄²	—	29	1	no	—
24	C₁₆	—	29	4	no	—
25	C₂×C₄	—	58	1	no	—
26	C₂×C₄	C₂×#1181	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	—	29	2	no	—
29	C₂²	#90796	1	1	yes	characteristic
30	C₄	—	116	1	no	—
31	C₄	C₄×#1181	1	1	yes	characteristic
32	C₄	#90800	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#11745218	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. #90770	C₄	semidirect
20. C₂₉	#347	semidirect

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