Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
738 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 153 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. C22×Q8×D67 | C2 | semidirect |
| 2. C2×#14524073 | C2 | semidirect |
| 4. #16863550 | C2 | semidirect |
| 5. #16863533 | C2 | semidirect |
| 6. #16863406 | C2 | semidirect |
| 7. #16863405 | C2 | semidirect |
| 8. #16863359 | C2 | semidirect |
| 9. C2×#137×C67 | C2 | semidirect |
| 19. C2×#11761618 | C22 | semidirect |
| 20. C2×#11761616 | C22 | semidirect |
| 28. #14523968 | C22 | semidirect |
| 29. #14523967 | C22 | semidirect |
| 34. C2×Q16×C67 | C22 | semidirect |
| 35. C2×SD16×C67 | C22 | semidirect |
| 42. C2×Dic134 | D4 | semidirect |
| 70. C2×Q8×C67 | D4 | semidirect |
| 127. C2×D67 | #137 | semidirect |
| 142. C67 | #3004 | semidirect |
| 145. C2×#137 | D67 | semidirect |
| 165. C2×Q16 | C2×D67 | semidirect |
| 167. C2×SD16 | C2×D67 | semidirect |
| 193. C2×Q8 | C22⋊D67 | semidirect |