Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 2. #41×Dic67 | C2 | semidirect |
| 3. #16863412 | C2 | semidirect |
| 4. C2×#14523969 | C2 | semidirect |
| 5. #568×C67 | C2 | semidirect |
| 7. #14524090 | C4 | semidirect |
| 8. #14524089 | C4 | semidirect |
| 14. #14524002 | C22 | semidirect |
| 15. C2×C4×Dic67 | C22 | semidirect |
| 16. #14523969 | C22 | semidirect |
| 17. #14523969 | C22 | semidirect |
| 20. C2×M16×C67 | C22 | semidirect |
| 24. #11761628 | C2×C4 | semidirect |
| 27. C2×Dic134 | C2×C4 | semidirect |
| 29. C2×D268 | C2×C4 | semidirect |
| 84. C67 | #2901 | semidirect |
| 86. #568 | D67 | semidirect |
| 98. C2×M16 | C2×D67 | semidirect |