Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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×#14523500 | C2 | semidirect |
| 3. #22553790 | C2 | semidirect |
| 4. #22553536 | C2 | semidirect |
| 5. #22553510 | C2 | semidirect |
| 6. #22553340 | C2 | semidirect |
| 7. #22553318 | C2 | semidirect |
| 8. #22553308 | C2 | semidirect |
| 9. C2×#137×C131 | C2 | semidirect |
| 19. Q8×Dic131 | C22 | semidirect |
| 23. Dic131⋊C8 | C22 | semidirect |
| 24. #16862170 | C22 | semidirect |
| 26. #16862167 | C22 | semidirect |
| 30. C2×Q16×C131 | C22 | semidirect |
| 31. C2×SD16×C131 | C22 | semidirect |
| 55. C2×Q8×C131 | D4 | semidirect |
| 116. C131 | #3043 | semidirect |
| 118. C2×#137 | D131 | semidirect |
| 131. C2×Q16 | C2×D131 | semidirect |
| 134. C2×SD16 | C2×D131 | semidirect |
| 155. C2×Q8 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523500 | 2 |
| #22553876 | 2 |
| #22553790 | 2 |
| #22553536 | 2 |
| #22553510 | 2 |
| #22553340 | 2 |
| #22553318 | 2 |
| #22553308 | 2 |
| C2×#137×C131 | 2 |
| #3043 | 131 |