Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16862279 | C2 | semidirect |
| 2. C2×#16862274 | C2 | semidirect |
| 3. C2×#16862268 | C2 | semidirect |
| 4. C22×#14523502 | C2 | semidirect |
| 5. #22553888 | C2 | semidirect |
| 6. #22553881 | C2 | semidirect |
| 7. #22553706 | C2 | semidirect |
| 8. #22553701 | C2 | semidirect |
| 9. #22553696 | C2 | semidirect |
| 10. #22553685 | C2 | semidirect |
| 11. #405×C131 | C2 | semidirect |
| 19. C2×Dic524 | C22 | semidirect |
| 20. C2×Dic524 | C22 | semidirect |
| 25. C2×#14523502 | C22 | semidirect |
| 26. C2×#14523502 | C22 | semidirect |
| 27. C2×#14523502 | C22 | semidirect |
| 29. C2×D1048 | C22 | semidirect |
| 30. #16862246 | C22 | semidirect |
| 33. #16862234 | C22 | semidirect |
| 41. #97×C131 | C22 | semidirect |
| 42. C4×C8×C131 | C22 | semidirect |
| 80. M16×C131 | D4 | semidirect |
| 81. C2×C8×C131 | D4 | semidirect |
| 148. C131 | #3154 | semidirect |
| 160. #405 | D131 | semidirect |
| 190. #97 | C2×D131 | semidirect |
| 191. C4×C8 | C2×D131 | semidirect |
| 226. M16 | D524 | semidirect |
| 227. C2×C8 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862279 | 2 |
| C2×#16862274 | 2 |
| C2×#16862268 | 2 |
| C22×#14523502 | 2 |
| #22553888 | 2 |
| #22553881 | 2 |
| #22553706 | 2 |
| #22553701 | 2 |
| #22553696 | 2 |
| #22553685 | 2 |
| #405×C131 | 2 |
| #3154 | 131 |