Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | AGL(1,𝔽7)2 |
| commutator, cosocle, hypocenter | C72 | C22×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C72×C13 | C22×C32 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C13 | |
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 |
|---|---|
| C13×ΓL(1,𝔽8)×AGL(1,𝔽7) | 2 |
| C13×ΓL(1,𝔽8)⋊AGL(1,𝔽7) | 2 |
| C13×D7×AGL(1,𝔽7) | 3 |
| C13×#64422⋊C2 | 3 |
| C13×#64423⋊C2 | 3 |
| C2×C3×C13×AGL(1,𝔽7) | 7 |
| AGL(1,𝔽7)2 | 13 |