Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
484 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 153 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. #22553217 | C2 | semidirect |
| 4. #22553217 | C2 | semidirect |
| 5. #22553196 | C2 | semidirect |
| 6. #22553181 | C2 | semidirect |
| 7. #22553177 | C2 | semidirect |
| 108. C131 | #2499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862225 | 2 |
| #22553240 | 2 |
| #22553217 | 2 |
| #22553196 | 2 |
| #22553181 | 2 |
| #22553177 | 2 |
| C4×C22⋊Dic131 | 2 |
| C2×#117×C131 | 2 |
| #2499 | 131 |