Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
425 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 425 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 3. #63646⋊C3 | C2 | semidirect |
| 4. #10592824 | C3 | semidirect |
| 17. #63646 | C2×C3 | semidirect |
| 126. H(3,𝔽3) | #430 | semidirect |
| 194. C32 | #5125 | semidirect |
| 195. C32 | C3×#430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×H(3,𝔽3) | 2 |
| C2×#3748⋊C3 | 2 |
| #63646⋊C3 | 2 |
| #10592824 | 3 |
| C3×#5125 | 3 |