Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 3. #22553790 | C2 | semidirect |
| 4. #22553536 | C2 | semidirect |
| 5. #22553520 | C2 | semidirect |
| 6. #22553338 | C2 | semidirect |
| 7. #22553321 | C2 | semidirect |
| 9. C22×Q16×C131 | C2 | semidirect |
| 111. C131 | #3044 | semidirect |
| 114. C22×Q16 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862277 | 2 |
| #22553886 | 2 |
| #22553790 | 2 |
| #22553536 | 2 |
| #22553520 | 2 |
| #22553338 | 2 |
| #22553321 | 2 |
| #22553309 | 2 |
| C22×Q16×C131 | 2 |
| #3044 | 131 |