Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 123 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 | #3324 |
| 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. #16864116 | C2 | semidirect |
| 3. #16863743 | C2 | semidirect |
| 4. #16863721 | C2 | semidirect |
| 5. #16863677 | C2 | semidirect |
| 6. #16863642 | C2 | semidirect |
| 7. #16863597 | C2 | semidirect |
| 8. #16863549 | C2 | semidirect |
| 9. C4×#11761617 | C2 | semidirect |
| 10. #16863402 | C2 | semidirect |
| 11. #436×C67 | C2 | semidirect |
| 15. C2×#11761617 | C22 | semidirect |
| 16. #14524043 | C22 | semidirect |
| 20. #14524022 | C22 | semidirect |
| 24. C4×Dic134 | C22 | semidirect |
| 27. #14524002 | C22 | semidirect |
| 28. #14523977 | C22 | semidirect |
| 29. #14523975 | C22 | semidirect |
| 30. #14523968 | C22 | semidirect |
| 33. #14523965 | C22 | semidirect |
| 34. #14523965 | C22 | semidirect |
| 35. #14523965 | C22 | semidirect |
| 36. C2×M16×C67 | C22 | semidirect |
| 38. C4⋊C8×C67 | C22 | semidirect |
| 39. C22⋊C8×C67 | C22 | semidirect |
| 40. C4×C8×C67 | C22 | semidirect |
| 136. C67 | #3324 | semidirect |
| 146. #436 | D67 | semidirect |
| 152. C2×M16 | C2×D67 | semidirect |
| 168. C4⋊C8 | C2×D67 | semidirect |
| 175. C22⋊C8 | C2×D67 | semidirect |
| 176. C4×C8 | C2×D67 | semidirect |