Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 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. C22×#14523501 | C2 | semidirect |
| 2. C2×#16862254 | C2 | semidirect |
| 3. #22553888 | C2 | semidirect |
| 5. #22553557 | C2 | semidirect |
| 6. #22553540 | C2 | semidirect |
| 7. #22553348 | C2 | semidirect |
| 8. #22553322 | C2 | semidirect |
| 9. #418×C131 | C2 | semidirect |
| 16. C2×#14523496 | C22 | semidirect |
| 18. C2×C8×D131 | C22 | semidirect |
| 24. #16862226 | C22 | semidirect |
| 28. #16862179 | C22 | semidirect |
| 29. #16862177 | C22 | semidirect |
| 30. #16862171 | C22 | semidirect |
| 50. C2×C131⋊C8 | D4 | semidirect |
| 120. C131 | #3057 | semidirect |
| 130. #418 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523501 | 2 |
| C2×#16862254 | 2 |
| #22553888 | 2 |
| #22553879 | 2 |
| #22553557 | 2 |
| #22553540 | 2 |
| #22553348 | 2 |
| #22553322 | 2 |
| #418×C131 | 2 |
| #3057 | 131 |