Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 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×D67 |
| commutator, socle | C22×C67 | C25 |
| Fitting | #519×C67 | C2 |
| hypercenter | #519 | D67 |
| hypocenter | C67 | #3487 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524091 | C2 | semidirect |
| 2. C22×#11761629 | C2 | semidirect |
| 3. #16864068 | C2 | semidirect |
| 4. #16864058 | C2 | semidirect |
| 5. #16863965 | C2 | semidirect |
| 6. #16863908 | C2 | semidirect |
| 7. #519×C67 | C2 | semidirect |
| 11. C2×#11761629 | C22 | semidirect |
| 13. C2×Q8×D67 | C22 | semidirect |
| 16. #14524040 | C22 | semidirect |
| 17. #14524031 | C22 | semidirect |
| 19. #14524023 | C22 | semidirect |
| 20. #14524018 | C22 | semidirect |
| 21. #14524018 | C22 | semidirect |
| 23. C4×D268 | C22 | semidirect |
| 25. C4×Q8×C67 | C22 | semidirect |
| 45. C2×Q8×C67 | D4 | semidirect |
| 88. C67 | #3487 | semidirect |
| 95. #519 | D67 | semidirect |
| 112. C4×Q8 | C2×D67 | semidirect |
| 121. C2×Q8 | D268 | semidirect |