Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14524068 | C2 | semidirect |
| 2. C22×D536 | C2 | semidirect |
| 3. #16863960 | C2 | semidirect |
| 4. #16863782 | C2 | semidirect |
| 5. #16863781 | C2 | semidirect |
| 6. #16863771 | C2 | semidirect |
| 7. #16863351 | C2 | semidirect |
| 8. C2×#135×C67 | C2 | semidirect |
| 11. C2×#11761615 | C22 | semidirect |
| 15. C2×#11761613 | C22 | semidirect |
| 17. #14524039 | C22 | semidirect |
| 18. #14524032 | C22 | semidirect |
| 22. #14523953 | C22 | semidirect |
| 23. C8×Dic67 | C22 | semidirect |
| 26. C2×Q16×C67 | C22 | semidirect |
| 27. C2×SD16×C67 | C22 | semidirect |
| 28. C2×D8×C67 | C22 | semidirect |
| 40. #11761612 | D4 | semidirect |
| 56. C2×C8×C67 | D4 | semidirect |
| 102. C67 | #3155 | semidirect |
| 104. C2×#135 | D67 | semidirect |
| 115. C2×Q16 | C2×D67 | semidirect |
| 117. C2×SD16 | C2×D67 | semidirect |
| 122. C2×D8 | C2×D67 | semidirect |
| 154. C2×C8 | C22⋊D67 | semidirect |