Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22553862 | C2 | semidirect |
| 2. C2×C4×D524 | C2 | semidirect |
| 3. #22553626 | C2 | semidirect |
| 4. #22553593 | C2 | semidirect |
| 5. #22553508 | C2 | semidirect |
| 6. #22553448 | C2 | semidirect |
| 7. C4×D1048 | C2 | semidirect |
| 8. #431×C131 | C2 | semidirect |
| 13. #16862246 | C22 | semidirect |
| 14. #16862243 | C22 | semidirect |
| 23. C4×D524 | C22 | semidirect |
| 26. #16862180 | C22 | semidirect |
| 28. #16862168 | C22 | semidirect |
| 30. C4⋊C8×C131 | C22 | semidirect |
| 32. C4×C8×C131 | C22 | semidirect |
| 76. D524 | #41 | semidirect |
| 87. C2×C4×C131 | D8 | semidirect |
| 120. C131 | #3100 | semidirect |
| 129. #431 | D131 | semidirect |
| 149. C4⋊C8 | C2×D131 | semidirect |
| 153. C4×C8 | C2×D131 | semidirect |
| 208. C2×C4 | D1048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553862 | 2 |
| C2×C4×D524 | 2 |
| #22553626 | 2 |
| #22553593 | 2 |
| #22553508 | 2 |
| #22553448 | 2 |
| C4×D1048 | 2 |
| #431×C131 | 2 |
| #3100 | 131 |