Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
282 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 10. C3×C3⋊(C3⋊C16) | C4 | semidirect |
| 46. C3⋊(C3⋊C16) | Dic3 | semidirect |
| 145. C33 | #365 | semidirect |
| 222. C32 | #4487 | semidirect |
| 223. C32 | #4494 | semidirect |
| 224. C32 | #4513 | semidirect |
| 252. C3 | #10589136 | semidirect |
| 253. C3 | #10589137 | semidirect |
| 254. C3 | #10589138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63646 | 2 |
| C3×#63644 | 2 |
| C3×#63639 | 2 |
| #10589138 | 3 |
| #10589137 | 3 |
| #10589136 | 3 |