Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
336 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22553688 | C2 | semidirect |
| 2. #22553507 | C2 | semidirect |
| 3. #22553056 | C2 | semidirect |
| 4. D4⋊(C131⋊C8) | C2 | semidirect |
| 5. D42×C131 | C2 | semidirect |
| 8. #16862243 | C22 | semidirect |
| 9. C4⋊(C131⋊C8) | C22 | semidirect |
| 11. C4×C131⋊C8 | C22 | semidirect |
| 50. D4×C131 | D8 | semidirect |
| 74. C131 | #1619 | semidirect |
| 76. D42 | D131 | semidirect |
| 123. D4 | #14523498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553688 | 2 |
| #22553507 | 2 |
| #22553056 | 2 |
| D4⋊(C131⋊C8) | 2 |
| D42×C131 | 2 |
| #1619 | 131 |