Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 2. C2×#16862275 | C2 | semidirect |
| 4. C4⋊Q8×D131 | C2 | semidirect |
| 5. #22553707 | C2 | semidirect |
| 6. #22553706 | C2 | semidirect |
| 7. #22553704 | C2 | semidirect |
| 8. #22553690 | C2 | semidirect |
| 9. #22553683 | C2 | semidirect |
| 10. #22553264 | C2 | semidirect |
| 11. #497×C131 | C2 | semidirect |
| 63. #14523496 | D4 | semidirect |
| 124. Dic131 | #137 | semidirect |
| 130. C131 | #3152 | semidirect |
| 139. #497 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862278 | 2 |
| C2×#16862275 | 2 |
| #22553861 | 2 |
| C4⋊Q8×D131 | 2 |
| #22553707 | 2 |
| #22553706 | 2 |
| #22553704 | 2 |
| #22553690 | 2 |
| #22553683 | 2 |
| #22553264 | 2 |
| #497×C131 | 2 |
| #3152 | 131 |