Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 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. #22553662 | C2 | semidirect |
| 3. #22553640 | C2 | semidirect |
| 4. #22553597 | C2 | semidirect |
| 5. #22553543 | C2 | semidirect |
| 6. #22553514 | C2 | semidirect |
| 7. #22553451 | C2 | semidirect |
| 8. C4×#14523500 | C2 | semidirect |
| 9. D4×C131⋊C8 | C2 | semidirect |
| 10. C2×#16862170 | C2 | semidirect |
| 11. D4×Q8×C131 | C2 | semidirect |
| 94. Q8×C131 | #41 | semidirect |
| 95. D4×C131 | SD16 | semidirect |
| 128. C131 | #3298 | semidirect |
| 130. D4×Q8 | D131 | semidirect |
| 213. Q8 | #14523512 | semidirect |
| 217. D4 | #14523500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553966 | 2 |
| #22553662 | 2 |
| #22553640 | 2 |
| #22553597 | 2 |
| #22553543 | 2 |
| #22553514 | 2 |
| #22553451 | 2 |
| C4×#14523500 | 2 |
| D4×C131⋊C8 | 2 |
| C2×#16862170 | 2 |
| D4×Q8×C131 | 2 |
| #3298 | 131 |