Subgroups — C₇×#338 #89380

Order 448.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×M₁₆	C₂	1	3	yes	maximal
2	C₂²×C₄×C₇	C₂²	1	1	yes	characteristic
3	C₇×M₁₆	—	2	6	no	—
4	C₂×C₇×C₈	C₄	1	6	yes	—
5	#338	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂³×C₇	Q₈	1	1	yes	characteristic
7	C₂×C₄×C₇	C₂×C₄	1	3	yes	—
8	C₂×C₄×C₇	D₄	1	3	yes	—
9	C₇×C₈	—	2	6	no	—
10	C₂×M₁₆	C₂×C₇	1	3	yes	—
11	C₂²×C₇	—	4	1	no	—
12	C₂²×C₇	C₄⋊C₄	1	3	yes	—
13	C₄×C₇	C₄²	1	1	yes	characteristic
14	C₄×C₇	C₂²⋊C₄	1	3	yes	—
15	C₂²×C₄	C₂²×C₇	1	1	yes	characteristic
16	M₁₆	—	2	6	no	—
17	C₂×C₈	C₄×C₇	1	6	yes	—
18	C₂×C₇	—	2	3	no	—
19	C₂×C₇	#95	1	1	yes	characteristic
20	C₂³	C₇×Q₈	1	1	yes	characteristic
21	C₂×C₄	C₂×C₄×C₇	1	3	yes	—
22	C₂×C₄	C₇×D₄	1	3	yes	—
23	C₈	—	2	6	no	—
24	C₇	#338	1	1	yes	characteristic, direct product factor, Sylow
25	C₂²	—	4	1	no	—
26	C₂²	C₇×C₄⋊C₄	1	3	yes	—
27	C₄	C₄²×C₇	1	1	yes	characteristic
28	C₄	C₇×C₂²⋊C₄	1	3	yes	—
29	C₂	—	2	3	no	—
30	C₂	C₇×#95	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. #338	C₇	direct (N × H)
24. C₇	#338	direct (N × H)

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

subgroup	index
C₂×C₇×M₁₆	2
#338	7