Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1492 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D61 |
| commutator, socle | C22×C61 | C25 |
| Fitting | C23×Q8×C61 | C2 |
| hypercenter | C23×Q8 | D61 |
| hypocenter | C61 | #3486 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519825 | C2 | semidirect |
| 2. Q8×C22⋊D61 | C2 | semidirect |
| 3. #16840423 | C2 | semidirect |
| 4. #16840336 | C2 | semidirect |
| 5. #16840273 | C2 | semidirect |
| 6. #16840240 | C2 | semidirect |
| 7. C23×Q8×C61 | C2 | semidirect |
| 9. C2×#11758226 | C22 | semidirect |
| 11. C2×Q8×D61 | C22 | semidirect |
| 12. #14519775 | C22 | semidirect |
| 13. #14519766 | C22 | semidirect |
| 16. #14519753 | C22 | semidirect |
| 19. Q8×Dic61 | C22 | semidirect |
| 30. C2×Q8×C61 | D4 | semidirect |
| 75. C22×C61 | 2−1+4 | semidirect |
| 90. C23×Q8 | D61 | semidirect |
| 96. C61 | #3486 | semidirect |
| 123. C2×Q8 | C22⋊D61 | semidirect |
| 166. C22 | #14519825 | semidirect |