Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4050 conjugacy classes of subgroups; only the 711 normal subgroups are shown.
This group has 4050 conjugacy classes of subgroups — too many to draw. Only its 711 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 |
|---|---|---|
| 2. C23×C3×C3⋊Dic3 | C2 | semidirect |
| 3. C2×#88814 | C2 | direct (N × H) |
| 8. C23×C3×C3⋊D3 | C4 | semidirect |
| 11. C22×C3×C3⋊Dic3 | C22 | semidirect |
| 12. #88814 | C22 | direct (N × H) |
| 16. C23×C3⋊Dic3 | D3 | semidirect |
| 27. C22×C3×C3⋊D3 | C2×C4 | semidirect |
| 30. C2×C3×C3⋊Dic3 | C23 | semidirect |
| 39. C23×C3⋊D3 | Dic3 | semidirect |
| 49. C22×C3⋊Dic3 | C2×D3 | semidirect |
| 58. C22×C33 | C22⋊C4 | semidirect |
| 64. C2×C3×C3⋊D3 | C22×C4 | semidirect |
| 94. C22×C3⋊D3 | C2×Dic3 | semidirect |
| 106. C2×C3⋊Dic3 | C22×D3 | semidirect |
| 114. C2×C33 | C2×C22⋊C4 | semidirect |
| 156. C22×C32 | (C2×D3)⋊C4 | semidirect |
| 157. C22×C32 | #217 | semidirect |
| 167. C2×C3⋊D3 | C22×Dic3 | semidirect |
| 182. C33 | C22×C22⋊C4 | semidirect |
| 231. C2×C32 | C2×(C2×D3)⋊C4 | semidirect |
| 232. C2×C32 | C2×#217 | semidirect |
| 264. C22×C3 | (C2×D3)⋊Dic3 | semidirect |
| 265. C22×C3 | #3722 | semidirect |
| 287. C32 | C22×(C2×D3)⋊C4 | semidirect |
| 288. C32 | C22×#217 | semidirect |
| 309. C2×C3 | C2×(C2×D3)⋊Dic3 | semidirect |
| 310. C2×C3 | C2×#3722 | semidirect |
| 321. C22 | #88814 | direct (N × H) |
| 329. C3 | C22×(C2×D3)⋊Dic3 | semidirect |
| 330. C3 | C22×#3722 | semidirect |
| 332. C2 | C2×#88814 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C3×C3⋊D3 | 2 |
| C23×C3×C3⋊Dic3 | 2 |
| C2×#88814 | 2 |
| C22×#3722 | 3 |
| C22×(C2×D3)⋊Dic3 | 3 |