Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
456 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×D244 |
| commutator | C4×C61 | C23×C4 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#405 | C2 |
| socle | C2×C61 | C2×C4×D4 |
| hypercenter | #405 | D61 |
| hypocenter | C61 | #2955 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C8 ◁ C22×C8 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14519783 | C2 | semidirect |
| 3. #16839885 | C2 | semidirect |
| 4. #16839880 | C2 | semidirect |
| 5. #16839811 | C2 | semidirect |
| 6. #16839780 | C2 | semidirect |
| 7. C61×#405 | C2 | semidirect |
| 9. #14519810 | C4 | semidirect |
| 10. #14519805 | C4 | semidirect |
| 14. #14519783 | C22 | semidirect |
| 15. #14519783 | C22 | semidirect |
| 19. #14519713 | C22 | semidirect |
| 20. #14519705 | C22 | semidirect |
| 24. #97×C61 | C22 | semidirect |
| 25. C4×C8×C61 | C22 | semidirect |
| 96. #405 | D61 | semidirect |
| 97. C61 | #2955 | semidirect |
| 114. #97 | C2×D61 | semidirect |
| 115. C4×C8 | C2×D61 | semidirect |