Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
888 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 290 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. #10592883 | C3 | direct (N × H) |
| 9. C33×Q16 | C4 | semidirect |
| 41. C32×Q16 | Dic3 | semidirect |
| 42. C32×Q16 | C3×C4 | semidirect |
| 101. C3×Q16 | C3×Dic3 | semidirect |
| 102. C3×Q16 | C3⋊Dic3 | semidirect |
| 137. C33 | #441 | semidirect |
| 166. Q16 | C3×C3⋊Dic3 | semidirect |
| 190. C32 | #5184 | semidirect |
| 191. C32 | C3×#441 | semidirect |
| 213. C3 | C3×#5184 | semidirect |
| 214. C3 | #10592883 | 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×Q8×C3⋊Dic3 | 2 |
| C3×#63662 | 2 |
| C3×#63644 | 2 |
| C3×#63642 | 2 |
| #10592883 | 3 |
| C3×#5184 | 3 |