Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D268 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #436×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #436 | D67 |
| hypocenter | C67 | #3273 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ #436 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524071 | C2 | semidirect |
| 2. #16864042 | C2 | semidirect |
| 3. #16863780 | C2 | semidirect |
| 4. #16863642 | C2 | semidirect |
| 5. #16863612 | C2 | semidirect |
| 6. #16863560 | C2 | semidirect |
| 7. #16863532 | C2 | semidirect |
| 8. C4×D536 | C2 | semidirect |
| 9. #436×C67 | C2 | semidirect |
| 11. C22×D268 | C22 | semidirect |
| 13. C2×Dic268 | C22 | semidirect |
| 14. C2×#11761617 | C22 | semidirect |
| 15. C2×#11761617 | C22 | semidirect |
| 19. #14524031 | C22 | semidirect |
| 21. #14524022 | C22 | semidirect |
| 25. C4×D268 | C22 | semidirect |
| 27. #14523977 | C22 | semidirect |
| 28. #14523968 | C22 | semidirect |
| 29. #14523965 | C22 | semidirect |
| 30. #14523965 | C22 | semidirect |
| 31. C2×M16×C67 | C22 | semidirect |
| 33. C4⋊C8×C67 | C22 | semidirect |
| 34. C22⋊C8×C67 | C22 | semidirect |
| 35. C4×C8×C67 | C22 | semidirect |
| 54. D536 | D4 | semidirect |
| 125. C67 | #3273 | semidirect |
| 134. #436 | D67 | semidirect |
| 144. C2×M16 | C2×D67 | semidirect |
| 155. C4⋊C8 | C2×D67 | semidirect |
| 159. C22⋊C8 | C2×D67 | semidirect |
| 160. C4×C8 | C2×D67 | semidirect |