Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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 | #405×C67 | C2 |
| socle | C22×C67 | C22×D4 |
| hypercenter | #405 | D67 |
| hypocenter | C67 | #3154 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524076 | C2 | semidirect |
| 2. C2×#14524071 | C2 | semidirect |
| 3. C2×#14524065 | C2 | semidirect |
| 4. C22×#11761617 | C2 | semidirect |
| 5. #16863972 | C2 | semidirect |
| 6. #16863965 | C2 | semidirect |
| 7. #16863790 | C2 | semidirect |
| 8. #16863785 | C2 | semidirect |
| 9. #16863780 | C2 | semidirect |
| 10. #16863769 | C2 | semidirect |
| 11. #405×C67 | C2 | semidirect |
| 19. C2×Dic268 | C22 | semidirect |
| 20. C2×Dic268 | C22 | semidirect |
| 25. C2×#11761617 | C22 | semidirect |
| 26. C2×#11761617 | C22 | semidirect |
| 27. C2×#11761617 | C22 | semidirect |
| 29. C2×D536 | C22 | semidirect |
| 30. #14524043 | C22 | semidirect |
| 33. #14524031 | C22 | semidirect |
| 41. #97×C67 | C22 | semidirect |
| 42. C4×C8×C67 | C22 | semidirect |
| 80. M16×C67 | D4 | semidirect |
| 81. C2×C8×C67 | D4 | semidirect |
| 149. C67 | #3154 | semidirect |
| 160. #405 | D67 | semidirect |
| 190. #97 | C2×D67 | semidirect |
| 191. C4×C8 | C2×D67 | semidirect |
| 226. M16 | D268 | semidirect |
| 227. C2×C8 | D268 | semidirect |