Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
366 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 4. #10589098 | C3 | direct (N × H) |
| 20. C3×C3⋊(C3⋊C8) | C8 | semidirect |
| 68. C3⋊(C3⋊C8) | C3×C8 | semidirect |
| 124. C33 | #334 | semidirect |
| 199. C32 | #4480 | semidirect |
| 200. C32 | C3×#334 | semidirect |
| 230. C3 | #10589098 | direct (N × H) |
| 231. C3 | C3×#4480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C3⋊(C3⋊C8) | 2 |
| C32×C4⋊(C3⋊C8) | 2 |
| C3×#4480 | 3 |
| #10589098 | 3 |