Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
384 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. #22553604 | C2 | semidirect |
| 5. #22553523 | C2 | semidirect |
| 6. #22553522 | C2 | semidirect |
| 8. #22553406 | C2 | semidirect |
| 9. #22553404 | C2 | semidirect |
| 11. #477×C131 | C2 | semidirect |
| 99. C4×D131 | Q16 | semidirect |
| 132. C131 | #3104 | semidirect |
| 138. #477 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553867 | 2 |
| C4×Q8×D131 | 2 |
| #22553649 | 2 |
| #22553604 | 2 |
| #22553523 | 2 |
| #22553522 | 2 |
| #22553469 | 2 |
| #22553406 | 2 |
| #22553404 | 2 |
| #22553364 | 2 |
| #477×C131 | 2 |
| #3104 | 131 |