Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22553061 | C2 | semidirect |
| 5. #22553060 | C2 | semidirect |
| 6. #22553060 | C2 | semidirect |
| 7. #333×C131 | C2 | semidirect |
| 88. C131 | #1548 | semidirect |
| 96. #333 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D131 | 2 |
| #22553364 | 2 |
| #22553334 | 2 |
| #22553061 | 2 |
| #22553060 | 2 |
| #333×C131 | 2 |
| #1548 | 131 |