Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D61 |
| commutator | C4×C61 | C23×C4 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#418 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #418 | D61 |
| hypocenter | C61 | #2949 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #418 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16840239 | C2 | semidirect |
| 4. #16839859 | C2 | semidirect |
| 5. #16839853 | C2 | semidirect |
| 6. #16839798 | C2 | semidirect |
| 7. #16839772 | C2 | semidirect |
| 8. #16839720 | C2 | semidirect |
| 11. C2×#11758200 | C4 | semidirect |
| 16. #14519742 | C22 | semidirect |
| 23. #14519710 | C22 | semidirect |
| 24. #14519708 | C22 | semidirect |
| 25. #14519702 | C22 | semidirect |
| 26. #14519687 | C22 | semidirect |
| 27. C8×Dic61 | C22 | semidirect |
| 42. C2×Dic122 | C2×C4 | semidirect |
| 52. #11758200 | C2×C4 | semidirect |
| 53. #11758200 | C2×C4 | semidirect |
| 60. C2×#92418 | C2×C4 | semidirect |
| 113. C61 | #2949 | semidirect |