Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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 | #423×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #423 | D67 |
| hypocenter | C67 | #3040 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524076 | C2 | semidirect |
| 3. C2×#14524031 | C2 | semidirect |
| 4. C4×#11761628 | C2 | semidirect |
| 5. #16863619 | C2 | semidirect |
| 6. #16863612 | C2 | semidirect |
| 7. #16863406 | C2 | semidirect |
| 8. #16863402 | C2 | semidirect |
| 9. #423×C67 | C2 | semidirect |
| 15. C2×Dic268 | C22 | semidirect |
| 17. C2×#11761617 | C22 | semidirect |
| 22. C4×Dic134 | C22 | semidirect |
| 23. C4×D268 | C22 | semidirect |
| 29. #14523968 | C22 | semidirect |
| 34. C4⋊C8×C67 | C22 | semidirect |
| 126. C67 | #3040 | semidirect |
| 133. #423 | D67 | semidirect |
| 158. C4⋊C8 | C2×D67 | semidirect |