Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. #22553640 | C2 | semidirect |
| 3. #22553599 | C2 | semidirect |
| 4. #22553514 | C2 | semidirect |
| 6. C4×#14523500 | C2 | semidirect |
| 7. #22553365 | C2 | semidirect |
| 8. #533×C131 | C2 | semidirect |
| 18. #16862177 | C22 | semidirect |
| 19. C4⋊(C131⋊C8) | C22 | semidirect |
| 20. #16862170 | C22 | semidirect |
| 23. C4×C131⋊C8 | C22 | semidirect |
| 24. C4⋊Q8×C131 | C22 | semidirect |
| 25. C4⋊Q8×C131 | C22 | semidirect |
| 30. C4×Q8×C131 | C22 | semidirect |
| 83. C2×C4×C131 | SD16 | semidirect |
| 112. C131 | #3101 | semidirect |
| 114. #533 | D131 | semidirect |
| 125. C4⋊Q8 | C2×D131 | semidirect |
| 126. C4⋊Q8 | C2×D131 | semidirect |
| 131. C4×Q8 | C2×D131 | semidirect |
| 195. C2×C4 | #14523500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D524 | 2 |
| #22553640 | 2 |
| #22553599 | 2 |
| #22553514 | 2 |
| #22553462 | 2 |
| C4×#14523500 | 2 |
| #22553365 | 2 |
| #533×C131 | 2 |
| #3101 | 131 |