Finite Group DatabasebetaFinite Group Databasebeta← ΓL(1,𝔽8)×C37×AGL(1,𝔽7) #45657412
Order 32634.
100 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | ΓL(1,𝔽8)×AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C72 | C2×C32×C37 |
| Frattini | C1 | G |
| Fitting, socle | C72×C37 | C2×C32 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C37 | |
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 |
|---|---|
| ΓL(1,𝔽8)2×C37 | 2 |
| D7×ΓL(1,𝔽8)×C37 | 3 |
| C37×#64422 | 3 |
| C37×#64423 | 3 |
| C7×C37×AGL(1,𝔽7) | 3 |
| C2×C3×ΓL(1,𝔽8)×C37 | 7 |
| C3×C37×AGL(1,𝔽7) | 7 |
| ΓL(1,𝔽8)×AGL(1,𝔽7) | 37 |