Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D67 |
| commutator | C4×C67 | C23×C4 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #442×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #442 | D67 |
| hypocenter | C67 | #2952 |
| LCS | G ▷ C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #442 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16863875 | C2 | semidirect |
| 3. #16863508 | C2 | semidirect |
| 4. #16863504 | C2 | semidirect |
| 5. #16863502 | C2 | semidirect |
| 6. #16863487 | C2 | semidirect |
| 7. C4×#11761616 | C2 | semidirect |
| 8. #106×D67 | C2 | semidirect |
| 9. #16863394 | C2 | semidirect |
| 10. #16863353 | C2 | semidirect |
| 11. #442×C67 | C2 | semidirect |
| 13. #14524062 | C4 | semidirect |
| 41. #11761627 | C2×C4 | semidirect |
| 48. Dic268 | C2×C4 | semidirect |
| 49. #11761616 | C2×C4 | semidirect |
| 53. C8×D67 | C2×C4 | semidirect |
| 66. D8×C67 | C2×C4 | semidirect |
| 115. C67 | #2952 | semidirect |
| 119. #442 | D67 | semidirect |
| 167. D8 | C4×D67 | semidirect |