Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
972 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 206 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. #10592882 | C3 | direct (N × H) |
| 66. C3×C3⋊Dic3 | Q16 | semidirect |
| 140. C3⋊Dic3 | C3×Q16 | semidirect |
| 148. C33 | #494 | semidirect |
| 206. C32 | #5183 | semidirect |
| 207. C32 | C3×#494 | semidirect |
| 231. C3 | C3×#5183 | semidirect |
| 232. C3 | #10592882 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q16 | 2 |
| C3×#64153 | 2 |
| C2×C3×#3756 | 2 |
| C2×C3×#3746 | 2 |
| C3×C8×C3⋊Dic3 | 2 |
| #10592882 | 3 |
| C3×#5183 | 3 |