Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
484 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 157 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. #22553218 | C2 | semidirect |
| 5. #22553218 | C2 | semidirect |
| 6. #22553197 | C2 | semidirect |
| 7. #22553182 | C2 | semidirect |
| 8. #22553178 | 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 |
| C2×#16862205 | 2 |
| #22553237 | 2 |
| #22553218 | 2 |
| #22553197 | 2 |
| #22553182 | 2 |
| #22553178 | 2 |
| C4×C22⋊C4×C131 | 2 |
| #2499 | 131 |