Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
384 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 173 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. #22553372 | C2 | semidirect |
| 3. #22553368 | C2 | semidirect |
| 4. #22553339 | C2 | semidirect |
| 7. M16×Dic131 | C2 | semidirect |
| 8. C2×#16862156 | C2 | semidirect |
| 9. #424×C131 | C2 | semidirect |
| 93. C131 | #2923 | semidirect |
| 99. #424 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553780 | 2 |
| #22553372 | 2 |
| #22553368 | 2 |
| #22553339 | 2 |
| #22553280 | 2 |
| #22553278 | 2 |
| M16×Dic131 | 2 |
| C2×#16862156 | 2 |
| #424×C131 | 2 |
| #2923 | 131 |