Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16862274 | C2 | semidirect |
| 2. C22×D1048 | C2 | semidirect |
| 3. C2×#16862252 | C2 | semidirect |
| 4. #22553583 | C2 | direct (N × H) |
| 5. C2×#16862162 | C2 | semidirect |
| 6. C2×#108×C131 | C2 | semidirect |
| 10. #16862274 | C22 | semidirect |
| 16. C2×D1048 | C22 | semidirect |
| 18. #16862252 | C22 | semidirect |
| 22. #16862162 | C22 | semidirect |
| 25. #108×C131 | C22 | semidirect |
| 104. C2×C131 | #472 | semidirect |
| 108. C131 | C2×#472 | semidirect |
| 114. C2×#108 | D131 | semidirect |
| 133. #108 | C2×D131 | semidirect |
| 215. C2 | #22553583 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862274 | 2 |
| C22×D1048 | 2 |
| C2×#16862252 | 2 |
| #22553583 | 2 |
| C2×#16862162 | 2 |
| C2×#108×C131 | 2 |
| C2×#472 | 131 |