Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22553276 | C2 | semidirect |
| 3. #22553048 | C2 | semidirect |
| 4. #22553045 | C2 | semidirect |
| 5. C2×#95×C131 | C2 | semidirect |
| 6. C2×#14523513 | C4 | semidirect |
| 9. #16862225 | C4 | semidirect |
| 11. #16862220 | C4 | semidirect |
| 16. #16862205 | C4 | semidirect |
| 24. C2×Dic262 | C2×C4 | semidirect |
| 25. C2×D524 | C2×C4 | semidirect |
| 32. C4⋊Dic131 | C2×C4 | semidirect |
| 33. C4⋊Dic131 | C2×C4 | semidirect |
| 119. C131 | #1504 | semidirect |
| 123. C2×#95 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553823 | 2 |
| #22553276 | 2 |
| #22553048 | 2 |
| #22553045 | 2 |
| C2×#95×C131 | 2 |
| #1504 | 131 |