Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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. #16863948 | C2 | semidirect |
| 3. #16863789 | C2 | semidirect |
| 4. #16863757 | C2 | semidirect |
| 5. #16863621 | C2 | semidirect |
| 6. #16863620 | C2 | semidirect |
| 7. #16863552 | C2 | semidirect |
| 10. #16863450 | C2 | semidirect |
| 11. #451×C67 | C2 | semidirect |
| 13. C2×#11761618 | C22 | semidirect |
| 16. #14524042 | C22 | semidirect |
| 17. #14524041 | C22 | semidirect |
| 25. Q8×Dic67 | C22 | semidirect |
| 27. #14524008 | C22 | semidirect |
| 32. Dic67⋊C8 | C22 | semidirect |
| 33. #14523967 | C22 | semidirect |
| 37. #14523953 | C22 | semidirect |
| 39. C2×Q16×C67 | C22 | semidirect |
| 41. #103×C67 | C22 | semidirect |
| 140. C67 | #3215 | semidirect |
| 148. #451 | D67 | semidirect |
| 155. C2×Q16 | C2×D67 | semidirect |
| 177. #103 | C2×D67 | semidirect |