Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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. #16864232 | C2 | semidirect |
| 2. C2×#14524071 | C2 | semidirect |
| 3. #16863960 | C2 | semidirect |
| 4. #16863571 | C2 | semidirect |
| 5. #16863566 | C2 | semidirect |
| 6. #16863412 | C2 | semidirect |
| 7. #413×C67 | C2 | semidirect |
| 8. #14524091 | C22 | semidirect |
| 12. #14524088 | C22 | semidirect |
| 16. C22×D268 | C22 | semidirect |
| 18. #14524071 | C22 | semidirect |
| 21. #14524039 | C22 | semidirect |
| 22. #14524032 | C22 | semidirect |
| 25. #14524002 | C22 | semidirect |
| 26. #14523969 | C22 | semidirect |
| 28. C2×M16×C67 | C22 | semidirect |
| 29. #101×C67 | C22 | semidirect |
| 30. #100×C67 | C22 | semidirect |
| 38. #11761628 | D4 | semidirect |
| 43. C2×Dic134 | D4 | semidirect |
| 49. C2×D268 | D4 | semidirect |
| 135. C67 | #3021 | semidirect |
| 142. #413 | D67 | semidirect |
| 157. C2×M16 | C2×D67 | semidirect |
| 164. #101 | C2×D67 | semidirect |
| 165. #100 | C2×D67 | semidirect |