Subgroups — #16812760

Order 3488.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13182038	C₂	1	2	yes	maximal
2	C₂×Dic₂₁₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₀₉	C₄	1	1	yes	characteristic
4	C₂×Dic₁₀₉	C₄	1	1	yes	characteristic
5	C₂×Dic₁₀₉	C₂²	1	1	yes	characteristic
6	Dic₂₁₈	—	2	2	no	—
7	#11724786	—	2	2	no	—
8	C₂²×C₁₀₉	C₂×C₄	1	1	yes	characteristic
9	C₄×C₁₀₉	—	2	1	no	—
10	Dic₁₀₉	—	2	1	no	—
11	Dic₁₀₉	D₄	1	2	yes	—
12	C₂×C₁₀₉	—	2	1	no	—
13	C₂×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
14	C₁₀₉	#101	1	1	yes	characteristic, complemented, Sylow
15	#101	—	109	1	no	maximal, Sylow
16	C₂×Q₈	—	109	1	no	—
17	M₁₆	—	109	2	no	—
18	Q₈	—	218	2	no	—
19	C₂×C₄	—	109	1	no	—
20	C₂×C₄	—	109	1	no	—
21	C₂×C₄	#89137	1	1	yes	characteristic
22	C₈	—	218	2	no	—
23	C₂²	C₂×#89137	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	—	109	2	no	—
26	C₄	—	218	1	no	—
27	C₂	—	2	1	no	—
28	C₂	C₂²⋊#89137	1	1	yes	characteristic

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

N	H ≅ G/N	type
14. C₁₀₉	#101	semidirect

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