Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524076 | C2 | semidirect |
| 2. C2×M16×D67 | C2 | semidirect |
| 4. C2×#14524023 | C2 | semidirect |
| 5. #16863655 | C2 | semidirect |
| 6. #16863643 | C2 | semidirect |
| 7. #16863638 | C2 | semidirect |
| 8. #16863626 | C2 | semidirect |
| 9. #16863404 | C2 | semidirect |
| 10. #16863395 | C2 | semidirect |
| 11. #428×C67 | C2 | semidirect |
| 16. C2×Dic268 | C22 | semidirect |
| 17. C2×#11761617 | C22 | semidirect |
| 36. #14523966 | C22 | semidirect |
| 37. #14523966 | C22 | semidirect |
| 38. #14523966 | C22 | semidirect |
| 39. #14523963 | C22 | semidirect |
| 43. #107×C67 | C22 | semidirect |
| 44. #106×C67 | C22 | semidirect |
| 84. M16×C67 | D4 | semidirect |
| 145. C2×D67 | #137 | semidirect |
| 164. C67 | #3056 | semidirect |
| 173. #428 | D67 | semidirect |
| 203. #107 | C2×D67 | semidirect |
| 204. #106 | C2×D67 | semidirect |
| 236. M16 | D268 | semidirect |