Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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×#16862276 | C2 | semidirect |
| 2. C2×#16862225 | C2 | semidirect |
| 3. #22553474 | C2 | semidirect |
| 4. #22553468 | C2 | semidirect |
| 5. #22553463 | C2 | semidirect |
| 6. #22553313 | C2 | semidirect |
| 7. #22553276 | C2 | semidirect |
| 9. C22×Dic262 | C22 | semidirect |
| 11. C2×#14523503 | C22 | semidirect |
| 12. C2×#14523501 | C22 | semidirect |
| 13. C2×#14523497 | C22 | semidirect |
| 17. #16862225 | C22 | semidirect |
| 18. C2×C4⋊Dic131 | C22 | semidirect |
| 21. #16862170 | C22 | semidirect |
| 22. #16862167 | C22 | semidirect |
| 24. C22⋊(C131⋊C8) | C22 | semidirect |
| 130. C22×C131 | #137 | semidirect |
| 146. C131 | #3007 | semidirect |
| 277. C22 | #16862276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862276 | 2 |
| C2×#16862225 | 2 |
| #22553474 | 2 |
| #22553468 | 2 |
| #22553463 | 2 |
| #22553313 | 2 |
| #22553276 | 2 |
| C22×#41×C131 | 2 |
| #3007 | 131 |