Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
454 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22553846 | C2 | semidirect |
| 2. C2×C4×D524 | C2 | semidirect |
| 3. #22553648 | C2 | semidirect |
| 4. #22553631 | C2 | semidirect |
| 5. #22553613 | C2 | semidirect |
| 6. #22553528 | C2 | semidirect |
| 7. #22553465 | C2 | semidirect |
| 9. C4×#14523502 | C2 | semidirect |
| 10. C4×D1048 | C2 | semidirect |
| 11. #431×C131 | C2 | semidirect |
| 17. #16862238 | C22 | semidirect |
| 18. #16862234 | C22 | semidirect |
| 22. C4×Dic262 | C22 | semidirect |
| 27. C4×D524 | C22 | semidirect |
| 32. #16862180 | C22 | semidirect |
| 33. #16862178 | C22 | semidirect |
| 34. #16862171 | C22 | semidirect |
| 37. #16862168 | C22 | semidirect |
| 39. C4⋊C8×C131 | C22 | semidirect |
| 42. C4×C8×C131 | C22 | semidirect |
| 140. C131 | #3105 | semidirect |
| 152. #431 | D131 | semidirect |
| 176. C4⋊C8 | C2×D131 | semidirect |
| 183. C4×C8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553846 | 2 |
| C2×C4×D524 | 2 |
| #22553648 | 2 |
| #22553631 | 2 |
| #22553613 | 2 |
| #22553528 | 2 |
| #22553465 | 2 |
| #22553448 | 2 |
| C4×#14523502 | 2 |
| C4×D1048 | 2 |
| #431×C131 | 2 |
| #3105 | 131 |