Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1080 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 565 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. #22553943 | C2 | direct (N × H) |
| 2. C2×#16862245 | C2 | semidirect |
| 3. C2×#16862237 | C2 | semidirect |
| 8. #16862245 | C22 | semidirect |
| 9. #16862237 | C22 | semidirect |
| 34. C22×C4×C131 | Q8 | semidirect |
| 53. C2×C4×C131 | C2×Q8 | semidirect |
| 69. C2×C131 | #544 | semidirect |
| 73. C131 | C2×#544 | semidirect |
| 102. C22×C4 | Dic262 | semidirect |
| 127. C2×C4 | C2×Dic262 | semidirect |
| 143. C2 | #22553943 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553943 | 2 |
| C2×#16862245 | 2 |
| C2×#16862237 | 2 |
| C2×#16862225 | 2 |
| C2×#16862205 | 2 |
| C22×C4⋊C4×C131 | 2 |
| C2×#544 | 131 |