Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
1492 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 553 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 | C61×#519 | C2 |
| hypercenter | #519 | D61 |
| hypocenter | C61 | #3486 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14519825 | C2 | semidirect |
| 2. C22×Q8×D61 | C2 | semidirect |
| 3. Q8×D244 | C2 | semidirect |
| 4. #16840424 | C2 | semidirect |
| 5. #16840338 | C2 | semidirect |
| 6. #16840274 | C2 | semidirect |
| 7. C61×#519 | C2 | semidirect |
| 9. C2×#11758226 | C22 | semidirect |
| 14. C2×Q8×D61 | C22 | semidirect |
| 16. #14519777 | C22 | semidirect |
| 17. #14519765 | C22 | semidirect |
| 20. #14519757 | C22 | semidirect |
| 25. C4×Q8×C61 | C22 | semidirect |
| 28. C2×Q8×C61 | D4 | semidirect |
| 78. C2×D61 | 2−1+4 | semidirect |
| 95. #519 | D61 | semidirect |
| 96. C61 | #3486 | semidirect |
| 113. C4×Q8 | C2×D61 | semidirect |
| 124. C2×Q8 | D244 | semidirect |