Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 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. C22×#14523502 | C2 | semidirect |
| 2. #22553883 | C2 | semidirect |
| 4. #22553558 | C2 | semidirect |
| 5. #22553541 | C2 | semidirect |
| 6. #22553350 | C2 | semidirect |
| 7. #22553322 | C2 | semidirect |
| 8. #22553318 | C2 | semidirect |
| 9. C2×#131×C131 | C2 | semidirect |
| 20. #16862225 | C22 | semidirect |
| 25. #16862180 | C22 | semidirect |
| 26. #16862178 | C22 | semidirect |
| 27. #16862171 | C22 | semidirect |
| 32. C2×M16×C131 | C22 | semidirect |
| 34. C22×C8×C131 | C22 | semidirect |
| 67. C2×C8×C131 | D4 | semidirect |
| 120. C131 | #3057 | semidirect |
| 123. C2×#131 | D131 | semidirect |
| 139. C2×M16 | C2×D131 | semidirect |
| 141. C22×C8 | C2×D131 | semidirect |
| 179. C2×C8 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523502 | 2 |
| #22553883 | 2 |
| #22553876 | 2 |
| #22553558 | 2 |
| #22553541 | 2 |
| #22553350 | 2 |
| #22553322 | 2 |
| #22553318 | 2 |
| C2×#131×C131 | 2 |
| #3057 | 131 |