Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
578 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22553785 | C2 | semidirect |
| 3. C2×#16862160 | C2 | semidirect |
| 4. #22553168 | C2 | semidirect |
| 5. #22553079 | C2 | semidirect |
| 6. #22553078 | C2 | semidirect |
| 7. #379×C131 | C2 | semidirect |
| 11. #16862215 | C4 | semidirect |
| 38. C22×Dic131 | D4 | semidirect |
| 48. C22⋊Dic131 | C2×C4 | semidirect |
| 58. C24×C131 | C2×C4 | semidirect |
| 61. C22×C4×C131 | D4 | semidirect |
| 70. C22×D131 | C22⋊C4 | semidirect |
| 84. C2×Dic131 | C22⋊C4 | semidirect |
| 160. C131 | #1889 | semidirect |
| 166. #379 | D131 | semidirect |
| 195. C24 | C4×D131 | semidirect |
| 211. C22×C4 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862215 | 2 |
| #22553785 | 2 |
| C2×#16862160 | 2 |
| #22553168 | 2 |
| #22553079 | 2 |
| #22553078 | 2 |
| #379×C131 | 2 |
| #1889 | 131 |