Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 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 | C2 | #121×D67 |
| commutator | C2×C4×C67 | C24 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | #472×C67 | C2 |
| socle | C2×C67 | C2×#121 |
| hypercenter | #472 | D67 |
| hypocenter | C67 | #3067 |
| LCS | G ▷ C2×C4×C67 ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #472 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16864192 | C2 | semidirect |
| 2. C2×#14524062 | C2 | semidirect |
| 3. #131×D67 | C2 | semidirect |
| 4. #16863672 | C2 | semidirect |
| 5. #16863671 | C2 | semidirect |
| 6. #16863663 | C2 | semidirect |
| 7. #16863658 | C2 | semidirect |
| 8. #16863657 | C2 | semidirect |
| 9. #108×D67 | C2 | semidirect |
| 10. #16863377 | C2 | semidirect |
| 11. #472×C67 | C2 | semidirect |
| 25. C2×Dic268 | C22 | semidirect |
| 26. C2×#11761616 | C22 | semidirect |
| 37. #14523979 | C22 | semidirect |
| 38. #14523978 | C22 | semidirect |
| 39. #14523961 | C22 | semidirect |
| 40. #14523961 | C22 | semidirect |
| 41. #14523960 | C22 | semidirect |
| 43. C2×D8×C67 | C22 | semidirect |
| 45. #108×C67 | C22 | semidirect |
| 46. #100×C67 | C22 | semidirect |
| 167. C67 | #3067 | semidirect |
| 174. #472 | D67 | semidirect |
| 195. C2×D8 | C2×D67 | semidirect |
| 209. #108 | C2×D67 | semidirect |
| 213. #100 | C2×D67 | semidirect |