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×#16862267 | C2 | semidirect |
| 2. #22553860 | C2 | semidirect |
| 3. C4×#14523514 | C2 | semidirect |
| 4. #22553532 | C2 | semidirect |
| 5. #22553526 | C2 | semidirect |
| 6. #22553522 | C2 | semidirect |
| 7. #22553518 | C2 | semidirect |
| 8. #22553504 | C2 | semidirect |
| 9. C4⋊C8×D131 | C2 | semidirect |
| 10. #22553305 | C2 | semidirect |
| 11. #460×C131 | C2 | semidirect |
| 45. #14523514 | D4 | semidirect |
| 136. C4×C131 | #135 | semidirect |
| 150. C131 | #3035 | semidirect |
| 159. #460 | D131 | semidirect |
| 292. C4 | #16862267 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862267 | 2 |
| #22553860 | 2 |
| C4×#14523514 | 2 |
| #22553532 | 2 |
| #22553526 | 2 |
| #22553522 | 2 |
| #22553518 | 2 |
| #22553504 | 2 |
| C4⋊C8×D131 | 2 |
| #22553305 | 2 |
| #460×C131 | 2 |
| #3035 | 131 |