Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
242 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 53 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. #11721330 | C2 | semidirect |
| 3. C9×H(3,𝔽4) | C3 | semidirect |
| 4. #10589552 | C3 | semidirect |
| 5. C9⋊(C22⋊A4) | C22 | semidirect |
| 10. C9×#120 | C2×C3 | semidirect |
| 11. #120⋊C9 | C2×C3 | semidirect |
| 17. C24×C9 | A4 | semidirect |
| 18. C24×C9 | C22×C3 | semidirect |
| 19. C22⋊(C22⋊C9) | C22×C3 | semidirect |
| 42. H(3,𝔽4) | 3−1+2 | semidirect |
| 69. #120 | C2×3−1+2 | semidirect |
| 84. C24 | C9⋊A4 | semidirect |
| 85. C24 | C22×3−1+2 | semidirect |
| 104. C9 | #5450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721330 | 2 |
| C3×#5450 | 3 |
| C9×H(3,𝔽4) | 3 |
| #10589552 | 3 |
| C22×C9⋊A4 | 4 |