Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
696 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 145 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×#390 | C2 |
| hypercenter | #390 | D61 |
| hypocenter | C61 | #2555 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519763 | C2 | semidirect |
| 2. C2×#14519750 | C2 | semidirect |
| 3. #16839682 | C2 | semidirect |
| 4. #16839679 | C2 | semidirect |
| 5. #16839670 | C2 | semidirect |
| 6. #16839650 | C2 | semidirect |
| 7. #16839638 | C2 | semidirect |
| 8. C4×#11758198 | C2 | semidirect |
| 9. C61×#390 | C2 | semidirect |
| 66. #11758198 | D4 | semidirect |
| 148. #390 | D61 | semidirect |
| 152. C61 | #2555 | semidirect |