Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
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. #22553354 | C2 | semidirect |
| 5. #22553177 | C2 | semidirect |
| 6. #22553073 | C2 | semidirect |
| 7. #343×C131 | C2 | semidirect |
| 19. #16862172 | C4 | semidirect |
| 47. C4×Dic131 | C2×C4 | semidirect |
| 53. M16×C131 | C2×C4 | semidirect |
| 111. C131 | #1860 | semidirect |
| 118. #343 | D131 | semidirect |
| 154. M16 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553793 | 2 |
| #22553354 | 2 |
| C2×#16862172 | 2 |
| #22553314 | 2 |
| #22553177 | 2 |
| #22553073 | 2 |
| #343×C131 | 2 |
| #1860 | 131 |