Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14524073 | C2 | semidirect |
| 2. C22×#11761616 | C2 | semidirect |
| 3. C2×#14524050 | C2 | semidirect |
| 4. #16863657 | C2 | direct (N × H) |
| 5. C2×#14523978 | C2 | semidirect |
| 6. C2×#14523961 | C2 | semidirect |
| 7. C2×#14523960 | C2 | semidirect |
| 11. #14524073 | C22 | semidirect |
| 17. C2×#11761616 | C22 | semidirect |
| 19. #14524050 | C22 | semidirect |
| 25. #14523978 | C22 | semidirect |
| 26. #14523961 | C22 | semidirect |
| 27. #14523960 | C22 | semidirect |
| 136. C2×C67 | #471 | semidirect |
| 139. C67 | C2×#471 | semidirect |
| 275. C2 | #16863657 | direct (N × H) |