Finite Group DatabasebetaFinite Group DatabasebetaOrder 22932.
248 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D7×#10587720 |
| commutator, cosocle, hypocenter | C72×C13 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C22×C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
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 |
|---|---|
| C3×D7×#63270 | 2 |
| C3×#16838470 | 2 |
| C3×C7×#10587720 | 2 |
| C3×C13×D72 | 3 |
| D7×#10587720 | 3 |
| C2×C3×D7×C13⋊C3 | 7 |
| C2×C3×#10587720 | 7 |
| C3×D7×AGL(1,𝔽7) | 13 |