Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #22553789 | C2 | semidirect |
| 4. #22553411 | C2 | semidirect |
| 5. #22553399 | C2 | semidirect |
| 6. #22553320 | C2 | semidirect |
| 8. #22553267 | C2 | semidirect |
| 9. #427×C131 | C2 | semidirect |
| 12. C2×#14523502 | C4 | semidirect |
| 17. #16862211 | C22 | semidirect |
| 23. #16862169 | C22 | semidirect |
| 25. #16862156 | C22 | semidirect |
| 26. C8×Dic131 | C22 | semidirect |
| 30. #107×C131 | C22 | semidirect |
| 31. #106×C131 | C22 | semidirect |
| 35. C2×Dic262 | C2×C4 | semidirect |
| 43. #14523502 | C2×C4 | semidirect |
| 44. #14523502 | C2×C4 | semidirect |
| 54. C2×C8×C131 | C2×C4 | semidirect |
| 103. C131 | #2949 | semidirect |
| 110. #427 | D131 | semidirect |
| 130. #107 | C2×D131 | semidirect |
| 131. #106 | C2×D131 | semidirect |
| 152. C2×C8 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523502 | 2 |
| #22553789 | 2 |
| #22553786 | 2 |
| #22553411 | 2 |
| #22553399 | 2 |
| #22553320 | 2 |
| #22553316 | 2 |
| #22553267 | 2 |
| #427×C131 | 2 |
| #2949 | 131 |