Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
306 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 8. C2×C3⋊AGL(1,𝔽9) | C4 | semidirect |
| 16. C2×C3×#157 | C8 | semidirect |
| 22. C2×C33×C4 | C8 | semidirect |
| 23. C2×C3×C3⋊Dic3 | C8 | semidirect |
| 53. C2×#157 | C3⋊C8 | semidirect |
| 61. C2×C32×C4 | C3⋊C8 | semidirect |
| 62. C2×C3⋊Dic3 | C3⋊C8 | semidirect |
| 109. C33 | #336 | semidirect |
| 124. C2×C3×C4 | AGL(1,𝔽9) | semidirect |
| 178. C32 | #4524 | semidirect |
| 190. C2×C4 | C3⋊AGL(1,𝔽9) | semidirect |
| 223. C3 | #10593267 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊AGL(1,𝔽9) | 2 |
| C2×C3×C4×#157 | 2 |
| #10593267 | 3 |
| #4524 | 9 |