Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. C22×#14523501 | C2 | semidirect |
| 2. #22553883 | C2 | semidirect |
| 3. #22553787 | C2 | semidirect |
| 4. #22553525 | C2 | semidirect |
| 5. #22553515 | C2 | semidirect |
| 6. #22553340 | C2 | semidirect |
| 7. #22553322 | C2 | semidirect |
| 8. #22553308 | C2 | semidirect |
| 14. #16862244 | C22 | semidirect |
| 15. #16862233 | C22 | semidirect |
| 23. Dic131⋊C8 | C22 | semidirect |
| 24. #16862171 | C22 | semidirect |
| 25. #16862170 | C22 | semidirect |
| 26. #16862167 | C22 | semidirect |
| 116. C131 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523501 | 2 |
| #22553883 | 2 |
| #22553787 | 2 |
| #22553525 | 2 |
| #22553515 | 2 |
| #22553340 | 2 |
| #22553322 | 2 |
| #22553308 | 2 |
| C2×AGL(1,ℤ/8)×C131 | 2 |
| #3042 | 131 |