Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 1. #22553714 | C2 | semidirect |
| 2. #22553136 | C2 | semidirect |
| 3. #22553133 | C2 | semidirect |
| 50. C131 | #2231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553714 | 2 |
| #22553136 | 2 |
| #22553133 | 2 |
| #22553122 | 2 |
| #443×C131 | 2 |
| #2231 | 131 |