Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 129 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×#16862268 | C2 | semidirect |
| 2. #22553755 | C2 | semidirect |
| 3. #22553750 | C2 | semidirect |
| 4. #22553744 | C2 | semidirect |
| 5. C2×M32×C131 | C2 | semidirect |
| 10. #16862268 | C22 | semidirect |
| 11. C2×Dic524 | C22 | semidirect |
| 13. C2×D1048 | C22 | semidirect |
| 14. Dic1048 | C22 | semidirect |
| 15. #16862191 | C22 | semidirect |
| 16. D2096 | C22 | semidirect |
| 18. M32×C131 | C22 | semidirect |
| 19. C2×C16×C131 | C22 | semidirect |
| 71. C131 | #3414 | semidirect |
| 77. C2×M32 | D131 | semidirect |
| 90. M32 | C2×D131 | semidirect |
| 91. C2×C16 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862268 | 2 |
| #22553755 | 2 |
| #22553750 | 2 |
| #22553744 | 2 |
| C2×M32×C131 | 2 |
| #3414 | 131 |