Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
326 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. #22553276 | C2 | semidirect |
| 3. #22553045 | C2 | semidirect |
| 4. #381×C131 | C2 | semidirect |
| 5. C22×D524 | C4 | semidirect |
| 10. #16862220 | C4 | semidirect |
| 12. C2×C4⋊Dic131 | C4 | semidirect |
| 15. C22⋊(C131⋊C8) | C22 | semidirect |
| 19. #95×C131 | C22 | semidirect |
| 102. C131 | #1510 | semidirect |
| 106. #381 | D131 | semidirect |
| 122. #95 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862220 | 2 |
| #22553276 | 2 |
| #22553045 | 2 |
| #381×C131 | 2 |
| #1510 | 131 |