Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
458 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 1. C32×H(3,𝔽4) | C3 | semidirect |
| 2. C3×#5465 | C3 | semidirect |
| 12. C24×C32 | A4 | semidirect |
| 14. C2×C32×Q8 | A4 | semidirect |
| 32. H(3,𝔽4) | H(3,𝔽3) | semidirect |
| 71. C24 | C22⋊H(3,𝔽3) | semidirect |
| 72. C2×Q8 | C22⋊H(3,𝔽3) | semidirect |
| 89. C32 | #5465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×H(3,𝔽4) | 3 |
| C3×#5465 | 3 |
| C22×C22⋊H(3,𝔽3) | 4 |
| C2×Q8⋊H(3,𝔽3) | 4 |