Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
582 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16862240 | C2 | semidirect |
| 2. #22553203 | C2 | semidirect |
| 3. #22553196 | C2 | semidirect |
| 5. #22553185 | C2 | semidirect |
| 6. #22553180 | C2 | semidirect |
| 7. C22×C42×C131 | C2 | semidirect |
| 40. C42×C131 | D4 | semidirect |
| 65. C22×C131 | #126 | semidirect |
| 82. C131 | #2852 | semidirect |
| 85. C22×C42 | D131 | semidirect |
| 123. C42 | C22⋊D131 | semidirect |
| 151. C22 | #16862240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862240 | 2 |
| #22553203 | 2 |
| #22553196 | 2 |
| #22553191 | 2 |
| #22553185 | 2 |
| #22553180 | 2 |
| C22×C42×C131 | 2 |
| #2852 | 131 |