Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. C2×#16862278 | C2 | semidirect |
| 3. C4×Q8×D131 | C2 | semidirect |
| 4. #22553537 | C2 | semidirect |
| 5. #22553536 | C2 | semidirect |
| 6. #22553519 | C2 | semidirect |
| 7. #22553513 | C2 | semidirect |
| 8. #22553512 | C2 | semidirect |
| 9. #22553334 | C2 | semidirect |
| 10. #22553312 | C2 | semidirect |
| 11. #462×C131 | C2 | semidirect |
| 49. Q8×D131 | D4 | semidirect |
| 133. C4×C131 | #137 | semidirect |
| 146. C131 | #3037 | semidirect |
| 154. #462 | D131 | semidirect |
| 285. 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 |
| #22553863 | 2 |
| C4×Q8×D131 | 2 |
| #22553537 | 2 |
| #22553536 | 2 |
| #22553519 | 2 |
| #22553513 | 2 |
| #22553512 | 2 |
| #22553334 | 2 |
| #22553312 | 2 |
| #462×C131 | 2 |
| #3037 | 131 |