Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16864103 | C2 | semidirect |
| 2. D4×Dic134 | C2 | semidirect |
| 3. #16863804 | C2 | semidirect |
| 4. #16863794 | C2 | semidirect |
| 5. #16863698 | C2 | semidirect |
| 6. #16863686 | C2 | semidirect |
| 7. #16863684 | C2 | semidirect |
| 8. #16863676 | C2 | semidirect |
| 9. #16863526 | C2 | semidirect |
| 65. D8×C67 | Q8 | semidirect |
| 78. D4×C67 | C2×Q8 | semidirect |
| 97. C8×C67 | C2×Q8 | semidirect |
| 122. C67 | #3384 | semidirect |
| 174. D8 | Dic134 | semidirect |
| 204. D4 | C2×Dic134 | semidirect |
| 220. C8 | C2×Dic134 | semidirect |