Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 83 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. #16863870 | C2 | semidirect |
| 3. #16863402 | C2 | semidirect |
| 4. #16863400 | C2 | semidirect |
| 5. C2×#14523959 | C2 | semidirect |
| 6. #16863156 | C2 | semidirect |
| 7. #339×C67 | C2 | semidirect |
| 13. #14524040 | C4 | semidirect |
| 38. C2×D268 | C2×C4 | semidirect |
| 44. C4⋊Dic67 | D4 | semidirect |
| 53. C4⋊C4×C67 | D4 | semidirect |
| 57. C42×C67 | C2×C4 | semidirect |
| 115. C67 | #1887 | semidirect |
| 122. #339 | D67 | semidirect |
| 165. C4⋊C4 | D268 | semidirect |
| 172. C42 | C4×D67 | semidirect |