Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22554129 | C2 | semidirect |
| 2. #22553752 | C2 | semidirect |
| 3. #22553748 | C2 | semidirect |
| 4. #22553742 | C2 | semidirect |
| 5. C2×#16862190 | C2 | semidirect |
| 6. #22553729 | C2 | semidirect |
| 7. #576×C131 | C2 | semidirect |
| 10. #16862268 | C22 | semidirect |
| 11. C2×Dic524 | C22 | semidirect |
| 12. #16862192 | C22 | semidirect |
| 13. #16862190 | C22 | semidirect |
| 14. #16862190 | C22 | semidirect |
| 15. #16862189 | C22 | semidirect |
| 16. #16862187 | C22 | semidirect |
| 17. #16862186 | C22 | semidirect |
| 18. C2×C131⋊C16 | C22 | semidirect |
| 74. C131 | #3416 | semidirect |
| 77. #576 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554129 | 2 |
| #22553752 | 2 |
| #22553748 | 2 |
| #22553742 | 2 |
| C2×#16862190 | 2 |
| #22553729 | 2 |
| #576×C131 | 2 |
| #3416 | 131 |