Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D244 |
| commutator | C4×C61 | C23×C4 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#405 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #405 | D61 |
| hypocenter | C61 | #2949 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16840239 | C2 | semidirect |
| 4. #16839864 | C2 | semidirect |
| 5. C4×#11758190 | C2 | semidirect |
| 6. #16839800 | C2 | semidirect |
| 7. #16839772 | C2 | semidirect |
| 9. C61×#405 | C2 | semidirect |
| 12. C2×#11758190 | C4 | semidirect |
| 15. C4×Dic122 | C22 | semidirect |
| 23. #14519711 | C22 | semidirect |
| 24. #14519709 | C22 | semidirect |
| 25. #14519702 | C22 | semidirect |
| 30. #97×C61 | C22 | semidirect |
| 31. C4×C8×C61 | C22 | semidirect |
| 42. C2×Dic122 | C2×C4 | semidirect |
| 45. C2×C8×C61 | C2×C4 | semidirect |
| 61. #11758190 | C2×C4 | semidirect |
| 62. #11758190 | C2×C4 | semidirect |
| 112. #405 | D61 | semidirect |
| 113. C61 | #2949 | semidirect |
| 134. #97 | C2×D61 | semidirect |
| 135. C4×C8 | C2×D61 | semidirect |
| 151. C2×C8 | C4×D61 | semidirect |