Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22553669 | C2 | semidirect |
| 4. #22553609 | C2 | semidirect |
| 5. #22553594 | C2 | semidirect |
| 6. #22553534 | C2 | semidirect |
| 8. Q8×C131⋊C8 | C2 | semidirect |
| 9. C4×#14523503 | C2 | semidirect |
| 10. C4×#14523500 | C2 | semidirect |
| 11. #557×C131 | C2 | semidirect |
| 117. C131 | #3365 | semidirect |
| 120. #557 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554047 | 2 |
| #22553669 | 2 |
| #22553660 | 2 |
| #22553609 | 2 |
| #22553594 | 2 |
| #22553534 | 2 |
| #22553512 | 2 |
| Q8×C131⋊C8 | 2 |
| C4×#14523503 | 2 |
| C4×#14523500 | 2 |
| #557×C131 | 2 |
| #3365 | 131 |