Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#16862243 | C2 | semidirect |
| 3. C4×#14523513 | C2 | semidirect |
| 4. #22553513 | C2 | semidirect |
| 5. #22553508 | C2 | semidirect |
| 6. #22553318 | C2 | semidirect |
| 7. #423×C131 | C2 | semidirect |
| 12. C2×#14523502 | C22 | semidirect |
| 13. C2×D1048 | C22 | semidirect |
| 17. C4×Dic262 | C22 | semidirect |
| 18. C4×D524 | C22 | semidirect |
| 23. #16862168 | C22 | semidirect |
| 26. C4⋊C8×C131 | C22 | semidirect |
| 29. #14523513 | D4 | semidirect |
| 62. Dic262 | C2×D4 | semidirect |
| 69. D524 | C2×D4 | semidirect |
| 94. C4×C131 | AGL(1,ℤ/8) | semidirect |
| 104. C131 | #3038 | semidirect |
| 111. #423 | D131 | semidirect |
| 130. C4⋊C8 | C2×D131 | semidirect |
| 201. C4 | #16862274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862274 | 2 |
| C2×#16862243 | 2 |
| C4×#14523513 | 2 |
| #22553513 | 2 |
| #22553508 | 2 |
| #22553318 | 2 |
| #423×C131 | 2 |
| #3038 | 131 |