Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16862293 | C2 | semidirect |
| 2. C22×#14523501 | C2 | semidirect |
| 3. #22553879 | C2 | semidirect |
| 4. #22553454 | C2 | semidirect |
| 5. #22553449 | C2 | semidirect |
| 6. #22553322 | C2 | semidirect |
| 7. #22553308 | C2 | semidirect |
| 8. #22553280 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C131 | C2 | semidirect |
| 15. C2×#14523512 | C22 | semidirect |
| 18. C2×Q8×D131 | C22 | semidirect |
| 27. #16862171 | C22 | semidirect |
| 28. #16862170 | C22 | semidirect |
| 29. #16862167 | C22 | semidirect |
| 30. (C2×D131)⋊C8 | C22 | semidirect |
| 48. C2×Dic262 | D4 | semidirect |
| 69. #41×C131 | D4 | semidirect |
| 145. C131 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D131 | semidirect |
| 191. #41 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862293 | 2 |
| C22×#14523501 | 2 |
| #22553879 | 2 |
| #22553454 | 2 |
| #22553449 | 2 |
| #22553322 | 2 |
| #22553308 | 2 |
| #22553280 | 2 |
| C2×AGL(1,ℤ/8)×C131 | 2 |
| #3010 | 131 |