Finite Group DatabasebetaFinite Group Databasebeta← AGL(1,𝔽7)×#10587720 #37524931
Order 22932.
248 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C13 | C22×C32 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 | |
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)×#10587720 | 2 |
| AGL(1,𝔽7)×#63270 | 2 |
| ΓL(1,𝔽8)⋊#10587720 | 2 |
| D7×#10587720 | 3 |
| C13×D7×AGL(1,𝔽7) | 3 |
| #21439620 | 3 |
| #21439612 | 3 |
| C2×C3×#10587720 | 7 |
| C2×C13⋊C3×AGL(1,𝔽7) | 7 |
| AGL(1,𝔽7)2 | 13 |