Subgroups — #30681069

Order 16807.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558883	C₇	1	1	yes	maximal, characteristic
2	C₃₄₃⋊C₇	C₇	1	6	yes	maximal, complemented
3	C₇×C₃₄₃	C₇	1	1	yes	maximal, characteristic, complemented
4	7₋¹⁺²	—	7	6	no	—
5	7₋¹⁺²	C₄₉	1	6	yes	—
6	H(3,𝔽₇)	C₄₉	1	1	yes	characteristic
7	C₇×C₄₉	—	7	1	no	—
8	C₇×C₄₉	C₇²	1	1	yes	characteristic
9	C₃₄₃	—	7	1	no	—
10	C₃₄₃	—	7	6	no	—
11	C₇²	—	7	1	no	—
12	C₇²	C₇×C₄₉	1	1	yes	characteristic
13	C₄₉	—	7	6	no	—
14	C₄₉	H(3,𝔽₇)	1	1	yes	characteristic
15	C₄₉	7₋¹⁺²	1	6	yes	—
16	C₇	—	7	1	no	—
17	C₇	—	49	1	no	—
18	C₇	C₇²⋊C₄₉	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₃₄₃⋊C₇	C₇	semidirect
3. C₇×C₃₄₃	C₇	semidirect

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