Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 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. #16863438 | C2 | semidirect |
| 5. #16863261 | C2 | semidirect |
| 6. #16863157 | C2 | semidirect |
| 7. #343×C67 | C2 | semidirect |
| 19. #14523969 | C4 | semidirect |
| 47. C4×Dic67 | C2×C4 | semidirect |
| 53. M16×C67 | C2×C4 | semidirect |
| 112. C67 | #1860 | semidirect |
| 118. #343 | D67 | semidirect |
| 154. M16 | C4×D67 | semidirect |