Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 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. D4×D524 | C2 | semidirect |
| 2. #22553688 | C2 | semidirect |
| 3. #22553504 | C2 | semidirect |
| 4. #22553055 | C2 | semidirect |
| 5. D4⋊(C131⋊C8) | C2 | semidirect |
| 6. #22553039 | C2 | semidirect |
| 7. #459×C131 | C2 | semidirect |
| 17. C4⋊(C131⋊C8) | C22 | semidirect |
| 19. C4×C131⋊C8 | C22 | semidirect |
| 21. #127×C131 | C22 | semidirect |
| 23. C4⋊C8×C131 | C22 | semidirect |
| 66. D524 | D8 | semidirect |
| 81. D4×C131 | D8 | semidirect |
| 117. C131 | #1619 | semidirect |
| 122. #459 | D131 | semidirect |
| 132. #127 | C2×D131 | semidirect |
| 139. C4⋊C8 | C2×D131 | semidirect |
| 194. D4 | #14523498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D524 | 2 |
| #22553688 | 2 |
| #22553504 | 2 |
| #22553055 | 2 |
| D4⋊(C131⋊C8) | 2 |
| #22553039 | 2 |
| #459×C131 | 2 |
| #1619 | 131 |