Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
271 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. C9×#557 | C3 | semidirect |
| 5. #557⋊C9 | C3 | semidirect |
| 19. C9×SL(2,𝔽3) | Q8 | semidirect |
| 21. #557⋊C3 | C9 | direct (N × H) |
| 59. #557 | C3×C9 | semidirect |
| 103. SL(2,𝔽3) | Q8×C9 | semidirect |
| 134. C9 | #557⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×SL(2,𝔽3) | 2 |
| C3×#557⋊C3 | 3 |
| C9×#557 | 3 |
| #557⋊C9 | 3 |
| C3×C9×C4⋊C4 | 4 |