Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 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. #16864125 | C2 | semidirect |
| 3. #16863803 | C2 | semidirect |
| 4. #16863801 | C2 | semidirect |
| 6. #16863689 | C2 | semidirect |
| 7. #16863681 | C2 | semidirect |
| 9. #16863526 | C2 | semidirect |
| 64. SD16×C67 | Q8 | semidirect |
| 75. Q8×C67 | C2×Q8 | semidirect |
| 95. C8×C67 | C2×Q8 | semidirect |
| 117. C67 | #3386 | semidirect |
| 167. SD16 | Dic134 | semidirect |
| 196. Q8 | C2×Dic134 | semidirect |
| 213. C8 | C2×Dic134 | semidirect |