Finite Group DatabasebetaFinite Group Databasebeta← C2×C7×ΓL(1,𝔽8)×D65 #50304281
Order 38220.
200 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 66 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×C7 | ΓL(1,𝔽8)×D65 |
| commutator, cosocle, hypocenter | C5×C7×C13 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72×C13 | C2×C3 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 ◁ C2×C7 | |
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×C5×C7×C13×ΓL(1,𝔽8) | 2 |
| C7×ΓL(1,𝔽8)×D65 | 2 |
| C2×C72×D65 | 3 |
| C2×C7×ΓL(1,𝔽8)×D13 | 5 |
| C2×C3×C7×D65 | 7 |
| C2×ΓL(1,𝔽8)×D65 | 7 |
| C2×C7×D5×ΓL(1,𝔽8) | 13 |