Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
345 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 112 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. #10592382 | C3 | semidirect |
| 113. H(3,𝔽3) | #499 | semidirect |
| 164. C32 | #4683 | semidirect |
| 165. C32 | C3×#499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64079⋊C3 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #63645⋊C3 | 2 |
| #63644⋊C3 | 2 |
| #10592382 | 3 |
| C3×#4683 | 3 |