Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C2×#16862252 | C2 | semidirect |
| 2. #22553886 | C2 | semidirect |
| 4. #22553555 | C2 | semidirect |
| 5. #22553538 | C2 | semidirect |
| 6. #22553350 | C2 | semidirect |
| 7. #22553321 | C2 | semidirect |
| 8. #22553317 | C2 | semidirect |
| 9. C22×SD16×C131 | C2 | semidirect |
| 13. C2×#14523496 | C22 | semidirect |
| 14. C2×C8×D131 | C22 | semidirect |
| 20. #16862222 | C22 | semidirect |
| 25. #16862180 | C22 | semidirect |
| 26. #16862178 | C22 | semidirect |
| 27. #16862170 | C22 | semidirect |
| 68. C2×C8×C131 | D4 | semidirect |
| 120. C131 | #3057 | semidirect |
| 122. C22×SD16 | D131 | semidirect |
| 180. C2×C8 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862252 | 2 |
| #22553886 | 2 |
| #22553879 | 2 |
| #22553555 | 2 |
| #22553538 | 2 |
| #22553350 | 2 |
| #22553321 | 2 |
| #22553317 | 2 |
| C22×SD16×C131 | 2 |
| #3057 | 131 |