Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 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. D4×Dic134 | C2 | semidirect |
| 2. #16863801 | C2 | semidirect |
| 3. #16863800 | C2 | semidirect |
| 4. #16863676 | C2 | semidirect |
| 5. #16863674 | C2 | semidirect |
| 6. C8×Dic134 | C2 | semidirect |
| 43. D8×C67 | Q8 | semidirect |
| 51. D4×C67 | C2×Q8 | semidirect |
| 63. Dic134 | D8 | direct (N × H) |
| 65. C8×C67 | C2×Q8 | semidirect |
| 84. C67 | Q8×D8 | semidirect |
| 119. D8 | Dic134 | direct (N × H) |
| 138. D4 | C2×Dic134 | semidirect |
| 150. C8 | C2×Dic134 | semidirect |