Finite Group DatabasebetaFinite Group DatabasebetaOrder 7776.
750 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 5. #72229255 | C2 | direct (N × H) |
| 22. C23×C22⋊C27 | C9 | semidirect |
| 52. C22×C22⋊C27 | C2×C9 | semidirect |
| 107. C2×C22⋊C27 | C22⋊C9 | semidirect |
| 179. C22⋊C27 | C2×C22⋊C9 | semidirect |
| 389. C25 | #6875 | semidirect |
| 472. C24 | C2×#6875 | semidirect |
| 539. C23 | #11757429 | semidirect |
| 540. C23 | #11757430 | semidirect |
| 574. C22 | C2×#11757429 | semidirect |
| 575. C22 | C2×#11757430 | semidirect |
| 584. C2 | #72229255 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9⋊(C22⋊(C22⋊C9)) | 3 |
| C2×#13048167 | 3 |
| C23×#66353 | 3 |
| #72229255 | 2 |
| C2×#11757430 | 4 |
| C2×#11757429 | 4 |