Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
674 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 6. #10590905 | C3 | direct (N × H) |
| 60. C3×C3⋊Dic3 | Q16 | semidirect |
| 143. C3⋊Dic3 | C3×Q16 | semidirect |
| 153. C33 | #494 | semidirect |
| 224. C32 | #5183 | semidirect |
| 225. C32 | C3×#494 | semidirect |
| 251. C3 | #10590905 | direct (N × H) |
| 252. C3 | C3×#5183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Dic12 | 2 |
| C3×#63873 | 2 |
| C2×C3×#3718 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| C3×#5183 | 3 |
| #10590905 | 3 |