Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22553619 | C2 | semidirect |
| 4. #22553522 | C2 | semidirect |
| 6. #22553417 | C2 | semidirect |
| 7. C4×#14523503 | C2 | semidirect |
| 95. C131 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553924 | 2 |
| #22553653 | 2 |
| #22553619 | 2 |
| #22553522 | 2 |
| #22553468 | 2 |
| #22553417 | 2 |
| C4×#14523503 | 2 |
| #22553373 | 2 |
| #519×C131 | 2 |
| #3127 | 131 |