Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
292 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator | C22×C61 | C22×C8 |
| Fitting | #95×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | #95 | #6923 |
| hypocenter | C61 | #1923 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4⋊#92420 | C2 | semidirect |
| 4. C2×C4×#92420 | C2 | semidirect |
| 5. #16840628 | C2 | semidirect |
| 6. #16840628 | C2 | semidirect |
| 49. #11758198 | C8 | semidirect |
| 130. C61 | #1923 | semidirect |