Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×Q8×Dic131 | C2 | semidirect |
| 3. #22553645 | C2 | semidirect |
| 5. #22553617 | C2 | semidirect |
| 6. #22553536 | C2 | semidirect |
| 8. #22553419 | C2 | semidirect |
| 9. #22553415 | C2 | semidirect |
| 10. #22553366 | C2 | semidirect |
| 11. #451×C131 | C2 | semidirect |
| 131. C131 | #3117 | semidirect |
| 139. #451 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553848 | 2 |
| C2×Q8×Dic131 | 2 |
| #22553645 | 2 |
| #22553631 | 2 |
| #22553617 | 2 |
| #22553536 | 2 |
| #22553451 | 2 |
| #22553419 | 2 |
| #22553415 | 2 |
| #22553366 | 2 |
| #451×C131 | 2 |
| #3117 | 131 |