Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
302 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 89 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. #16863436 | C2 | semidirect |
| 4. #16863265 | C2 | semidirect |
| 5. #16863164 | C2 | semidirect |
| 6. #16863157 | C2 | semidirect |
| 20. #14523970 | C4 | semidirect |
| 30. #11761612 | C2×C4 | semidirect |
| 43. C4×Dic67 | C2×C4 | semidirect |
| 62. Q8×C67 | C4⋊C4 | semidirect |
| 66. D4×C67 | C4⋊C4 | semidirect |
| 113. C67 | #1859 | semidirect |
| 175. Q8 | Dic67⋊C4 | semidirect |
| 179. D4 | Dic67⋊C4 | semidirect |