Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16862269 | C2 | semidirect |
| 2. #22553863 | C2 | semidirect |
| 3. C4×#14523514 | C2 | semidirect |
| 4. #22553536 | C2 | semidirect |
| 5. #22553530 | C2 | semidirect |
| 6. #22553514 | C2 | semidirect |
| 7. #22553512 | C2 | semidirect |
| 8. #22553508 | C2 | semidirect |
| 9. C4⋊C8×D131 | C2 | semidirect |
| 10. #22553307 | C2 | semidirect |
| 11. #462×C131 | C2 | semidirect |
| 47. #14523514 | D4 | semidirect |
| 137. C4×C131 | #135 | semidirect |
| 150. C131 | #3035 | semidirect |
| 157. #462 | D131 | semidirect |
| 292. C4 | #16862269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862269 | 2 |
| #22553863 | 2 |
| C4×#14523514 | 2 |
| #22553536 | 2 |
| #22553530 | 2 |
| #22553514 | 2 |
| #22553512 | 2 |
| #22553508 | 2 |
| C4⋊C8×D131 | 2 |
| #22553307 | 2 |
| #462×C131 | 2 |
| #3035 | 131 |