Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1056 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 169 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 | C23×D61 |
| commutator, socle | C23×C61 | C24 |
| Fitting | C61×#381 | C2 |
| hypercenter | #381 | D61 |
| hypocenter | C61 | #2404 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11758222 | C2 | semidirect |
| 2. C2×#14519747 | C2 | semidirect |
| 3. C22×#11758198 | C2 | semidirect |
| 4. #16839675 | C2 | semidirect |
| 5. #16839672 | C2 | semidirect |
| 6. #16839640 | C2 | semidirect |
| 7. #16839639 | C2 | semidirect |
| 8. C61×#381 | C2 | semidirect |
| 12. C22×Dic122 | C22 | semidirect |
| 14. C22×D244 | C22 | semidirect |
| 17. C22×C4×D61 | C22 | semidirect |
| 23. C2×#11758198 | C22 | semidirect |
| 24. #14519684 | C22 | semidirect |
| 27. #95×C61 | C22 | semidirect |
| 28. #95×C61 | C22 | semidirect |
| 37. C22×C4×C61 | D4 | semidirect |
| 43. C2×C22⋊D61 | D4 | semidirect |
| 82. C22×D61 | #41 | semidirect |
| 141. #381 | D61 | semidirect |
| 142. C61 | #2404 | semidirect |
| 161. #95 | C2×D61 | semidirect |
| 162. #95 | C2×D61 | semidirect |
| 189. C22×C4 | D244 | semidirect |