Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1224 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 209 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 | C2×#120×C61 | C2 |
| hypercenter | C2×#120 | D61 |
| hypocenter | C61 | #2847 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic61 | C2 | semidirect |
| 2. C2×#14519749 | C2 | semidirect |
| 3. C2×#14519746 | C2 | semidirect |
| 4. #16839642 | C2 | semidirect |
| 5. #16839639 | C2 | semidirect |
| 6. #16839620 | C2 | semidirect |
| 7. C2×#120×C61 | C2 | semidirect |
| 9. C22×C22⋊D61 | C22 | semidirect |
| 15. C2×#11758196 | C22 | semidirect |
| 17. C2×C22⋊Dic61 | C22 | semidirect |
| 18. C2×#11758198 | C22 | semidirect |
| 19. #14519684 | C22 | semidirect |
| 26. C24×C61 | D4 | semidirect |
| 42. C22×Dic61 | D4 | semidirect |
| 88. C22×C61 | #121 | semidirect |
| 98. Dic61 | #120 | semidirect |
| 109. C2×#120 | D61 | semidirect |
| 113. C61 | #2847 | semidirect |
| 133. C24 | C22⋊D61 | semidirect |
| 197. C22 | #14519749 | semidirect |