Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
475 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 475 conjugacy classes of subgroups — too many to draw. Only its 148 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. #63641⋊C3 | C2 | semidirect |
| 5. #10592801 | C3 | semidirect |
| 22. #63641 | C2×C3 | semidirect |
| 151. H(3,𝔽3) | #424 | semidirect |
| 227. C32 | #5102 | semidirect |
| 228. C32 | C3×#424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×H(3,𝔽3) | 2 |
| #64135⋊C3 | 2 |
| C2×#3748⋊C3 | 2 |
| #63641⋊C3 | 2 |
| #10592801 | 3 |
| C3×#5102 | 3 |