Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1102 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 213 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×#16862229 | C2 | semidirect |
| 3. #22553191 | C2 | semidirect |
| 4. #22553185 | C2 | semidirect |
| 5. #22553175 | C2 | semidirect |
| 6. #22553168 | C2 | semidirect |
| 7. C24×C4×C131 | C2 | semidirect |
| 12. C2×Dic131⋊C4 | C22 | semidirect |
| 17. C2×(C2×D131)⋊C4 | C22 | semidirect |
| 18. C131⋊#95 | C22 | semidirect |
| 48. C22×C4×C131 | D4 | semidirect |
| 84. C22×C131 | #123 | semidirect |
| 101. C131 | #2849 | semidirect |
| 103. C24×C4 | D131 | semidirect |
| 144. C22×C4 | C22⋊D131 | semidirect |
| 189. C22 | #16862229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862229 | 2 |
| C2×#16862215 | 2 |
| #22553191 | 2 |
| #22553185 | 2 |
| #22553175 | 2 |
| #22553168 | 2 |
| C24×C4×C131 | 2 |
| #2849 | 131 |