Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 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. C2×#16862233 | C2 | semidirect |
| 4. #22553780 | C2 | semidirect |
| 5. #22553533 | C2 | semidirect |
| 6. #22553526 | C2 | semidirect |
| 7. #22553335 | C2 | semidirect |
| 8. #22553320 | C2 | semidirect |
| 9. #418×C131 | C2 | semidirect |
| 14. C2×Dic524 | C22 | semidirect |
| 15. C2×#14523502 | C22 | semidirect |
| 22. #16862211 | C22 | semidirect |
| 23. #16862208 | C22 | semidirect |
| 29. Dic131⋊C8 | C22 | semidirect |
| 30. #16862169 | C22 | semidirect |
| 125. C131 | #3040 | semidirect |
| 135. #418 | 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×#16862272 | 2 |
| C2×#16862233 | 2 |
| #22553780 | 2 |
| #22553533 | 2 |
| #22553526 | 2 |
| #22553335 | 2 |
| #22553320 | 2 |
| #418×C131 | 2 |
| #3040 | 131 |