Finite Group DatabasebetaFinite Group Databasebeta← C2×ΓL(1,𝔽8)⋊#11716327 #45692147
Order 33516.
280 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ΓL(1,𝔽8)⋊#11716327 |
| commutator, cosocle, hypocenter | C72×C19 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C19 | C2×C32 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×ΓL(1,𝔽8)×#87704 | 2 |
| ΓL(1,𝔽8)⋊#11716327 | 2 |
| C2×ΓL(1,𝔽8)⋊D133 | 3 |
| C2×#19150306 | 3 |
| C2×#19150290 | 3 |
| C2×#19150284 | 3 |
| C2×C3×#11716327 | 7 |
| C2×ΓL(1,𝔽8)⋊(D19⋊C3) | 7 |
| C2×ΓL(1,𝔽8)⋊AGL(1,𝔽7) | 19 |