Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#16862279 | C2 | semidirect |
| 3. #22553883 | C2 | semidirect |
| 4. #22553793 | C2 | semidirect |
| 5. #22553533 | C2 | semidirect |
| 6. #22553526 | C2 | semidirect |
| 7. #22553521 | C2 | semidirect |
| 8. #22553516 | C2 | semidirect |
| 9. #22553340 | C2 | semidirect |
| 10. C2×#16862169 | C2 | semidirect |
| 11. #417×C131 | C2 | semidirect |
| 146. C131 | #3046 | semidirect |
| 157. #417 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862279 | 2 |
| C2×#16862266 | 2 |
| #22553883 | 2 |
| #22553793 | 2 |
| #22553533 | 2 |
| #22553526 | 2 |
| #22553521 | 2 |
| #22553516 | 2 |
| #22553340 | 2 |
| C2×#16862169 | 2 |
| #417×C131 | 2 |
| #3046 | 131 |