Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#14524041 | C2 | semidirect |
| 4. #16863599 | C2 | direct (N × H) |
| 5. C2×Dic67⋊C8 | C2 | semidirect |
| 6. C2×#14523968 | C2 | semidirect |
| 7. C2×#14523967 | C2 | semidirect |
| 15. #14524041 | C22 | semidirect |
| 23. Dic67⋊C8 | C22 | semidirect |
| 24. #14523968 | C22 | semidirect |
| 25. #14523967 | C22 | semidirect |
| 88. C2×Dic67 | SD16 | semidirect |
| 111. Dic67 | C2×SD16 | semidirect |
| 113. C2×C67 | #461 | semidirect |
| 118. C67 | C2×#461 | semidirect |
| 231. C2 | #16863599 | direct (N × H) |