Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
138 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 15. C33×C8 | C8 | semidirect |
| 16. C3×C3⋊(C3⋊C8) | C8 | semidirect |
| 39. C32×C8 | C3⋊C8 | semidirect |
| 40. C3⋊(C3⋊C8) | C3⋊C8 | semidirect |
| 63. C33 | #335 | semidirect |
| 72. C3×C8 | AGL(1,𝔽9) | semidirect |
| 98. C32 | #4458 | semidirect |
| 105. C8 | C3⋊AGL(1,𝔽9) | semidirect |
| 121. C3 | #10593253 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊(C3⋊AGL(1,𝔽9)) | 2 |
| C3×C8×#157 | 2 |
| #10593253 | 3 |
| #4458 | 9 |