Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22554040 | C2 | semidirect |
| 3. #22553667 | C2 | semidirect |
| 5. #22553613 | C2 | semidirect |
| 6. #22553598 | C2 | semidirect |
| 7. #22553535 | C2 | semidirect |
| 9. C4×Dic524 | C2 | semidirect |
| 10. C4×#14523502 | C2 | semidirect |
| 11. C8×Q8×C131 | C2 | semidirect |
| 117. C131 | #3365 | semidirect |
| 127. C8×Q8 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554047 | 2 |
| #22554040 | 2 |
| #22553667 | 2 |
| #22553659 | 2 |
| #22553613 | 2 |
| #22553598 | 2 |
| #22553535 | 2 |
| #22553513 | 2 |
| C4×Dic524 | 2 |
| C4×#14523502 | 2 |
| C8×Q8×C131 | 2 |
| #3365 | 131 |