Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#16862179 | C2 | semidirect |
| 5. #22553075 | C2 | semidirect |
| 6. #22553074 | C2 | semidirect |
| 7. C2×#107×C131 | C2 | semidirect |
| 18. (C2×D131)⋊C8 | C4 | semidirect |
| 39. C2×C131⋊C8 | C2×C4 | semidirect |
| 51. C2×C8×C131 | C2×C4 | semidirect |
| 105. C2×D131 | #107 | semidirect |
| 123. C131 | #1852 | semidirect |
| 127. C2×#107 | D131 | semidirect |
| 169. C2×C8 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D131 | 2 |
| C2×#16862179 | 2 |
| C2×(C2×D131)⋊C8 | 2 |
| #22553169 | 2 |
| #22553075 | 2 |
| #22553074 | 2 |
| C2×#107×C131 | 2 |
| #1852 | 131 |