Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
740 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 2. C2×Q16×D131 | C2 | semidirect |
| 4. #22553470 | C2 | semidirect |
| 5. #22553469 | C2 | semidirect |
| 6. #22553468 | C2 | semidirect |
| 7. #22553467 | C2 | semidirect |
| 8. #22553466 | C2 | semidirect |
| 9. #103×D131 | C2 | semidirect |
| 11. #451×C131 | C2 | semidirect |
| 22. C2×Dic524 | C22 | semidirect |
| 23. C2×#14523503 | C22 | semidirect |
| 24. C2×#14523503 | 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 |
| 99. C22×D131 | Q16 | semidirect |
| 140. C22×C131 | C2×Q16 | semidirect |
| 147. C2×D131 | C2×Q16 | semidirect |
| 164. D131 | #451 | direct (N × H) |
| 165. C131 | C2×#451 | semidirect |
| 175. #451 | D131 | direct (N × H) |
| 193. C2×Q16 | C2×D131 | semidirect |
| 207. #103 | C2×D131 | semidirect |
| 313. C22 | Q16×D131 | 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×Q16×D131 | 2 |
| C22⋊Q8×D131 | 2 |
| #22553470 | 2 |
| #22553469 | 2 |
| #22553468 | 2 |
| #22553467 | 2 |
| #22553466 | 2 |
| #103×D131 | 2 |
| C22⋊C8×D131 | 2 |
| #451×C131 | 2 |
| C2×#451 | 131 |