Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 2. C4⋊Q8×D131 | C2 | semidirect |
| 4. #22553522 | C2 | semidirect |
| 5. #22553520 | C2 | semidirect |
| 6. #22553518 | C2 | semidirect |
| 7. #22553516 | C2 | semidirect |
| 8. #22553514 | C2 | semidirect |
| 9. #22553334 | C2 | semidirect |
| 10. #22553319 | C2 | semidirect |
| 11. #462×C131 | C2 | semidirect |
| 132. C4×C131 | #137 | semidirect |
| 139. Dic131 | #137 | semidirect |
| 145. C131 | #3039 | semidirect |
| 152. #462 | D131 | semidirect |
| 283. C4 | #16862278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862278 | 2 |
| C4⋊Q8×D131 | 2 |
| C4×#14523514 | 2 |
| #22553522 | 2 |
| #22553520 | 2 |
| #22553518 | 2 |
| #22553516 | 2 |
| #22553514 | 2 |
| #22553334 | 2 |
| #22553319 | 2 |
| #462×C131 | 2 |
| #3039 | 131 |