Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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×Q8×D131 | C2 | semidirect |
| 2. C2×#16862278 | C2 | semidirect |
| 4. #22553467 | C2 | semidirect |
| 5. #22553466 | C2 | semidirect |
| 6. #22553453 | C2 | semidirect |
| 7. #22553452 | C2 | semidirect |
| 8. #22553451 | C2 | semidirect |
| 9. #22553319 | C2 | semidirect |
| 10. #22553274 | C2 | semidirect |
| 11. #451×C131 | C2 | semidirect |
| 23. C2×#14523503 | C22 | semidirect |
| 24. C2×#14523502 | C22 | semidirect |
| 25. C2×#14523500 | C22 | semidirect |
| 35. #16862171 | C22 | semidirect |
| 36. #16862170 | C22 | semidirect |
| 37. #16862169 | C22 | semidirect |
| 41. C2×Q16×C131 | C22 | semidirect |
| 43. #103×C131 | C22 | semidirect |
| 58. Q8×D131 | D4 | semidirect |
| 141. C22×C131 | #137 | semidirect |
| 152. C2×D131 | #137 | semidirect |
| 169. C131 | #3004 | semidirect |
| 176. #451 | D131 | semidirect |
| 195. C2×Q16 | C2×D131 | semidirect |
| 211. #103 | C2×D131 | semidirect |
| 321. C22 | #16862278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D131 | 2 |
| C2×#16862278 | 2 |
| #22553825 | 2 |
| #22553467 | 2 |
| #22553466 | 2 |
| #22553453 | 2 |
| #22553452 | 2 |
| #22553451 | 2 |
| #22553319 | 2 |
| #22553274 | 2 |
| #451×C131 | 2 |
| #3004 | 131 |