Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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. #22553135 | C2 | semidirect |
| 4. #22553129 | C2 | semidirect |
| 51. C131 | #2239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553570 | 2 |
| #22553361 | 2 |
| #22553135 | 2 |
| #22553129 | 2 |
| #349×C131 | 2 |
| #2239 | 131 |