Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1416 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 1416 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 |
|---|---|---|
| 4. C2×Dic3⋊#157 | C2 | direct (N × H) |
| 11. C22×C3⋊(C3⋊Dic3) | C4 | semidirect |
| 12. C22×C32×Dic3 | C4 | semidirect |
| 13. C2×Dic3×C3⋊D3 | C4 | semidirect |
| 15. Dic3⋊#157 | C22 | direct (N × H) |
| 30. C2×C3⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 31. C2×C32×Dic3 | C2×C4 | semidirect |
| 32. Dic3×C3⋊D3 | C2×C4 | semidirect |
| 51. C22×C33 | C4⋊C4 | semidirect |
| 53. C2×C3×C3⋊D3 | C4⋊C4 | semidirect |
| 60. C3⋊(C3⋊Dic3) | C22×C4 | semidirect |
| 61. C32×Dic3 | C22×C4 | semidirect |
| 92. C2×C33 | C2×C4⋊C4 | semidirect |
| 94. C3×C3⋊D3 | C2×C4⋊C4 | semidirect |
| 109. C22×Dic3 | #157 | semidirect |
| 117. C22×C32 | Dic3⋊C4 | semidirect |
| 119. C2×C3⋊D3 | Dic3⋊C4 | semidirect |
| 140. C33 | C22×C4⋊C4 | semidirect |
| 162. C2×Dic3 | C2×#157 | semidirect |
| 169. C2×C32 | C2×Dic3⋊C4 | semidirect |
| 171. C3⋊D3 | C2×Dic3⋊C4 | semidirect |
| 196. C22×C3 | C4⋊#157 | semidirect |
| 209. Dic3 | C22×#157 | semidirect |
| 212. C32 | C22×Dic3⋊C4 | semidirect |
| 233. C2×C3 | C2×C4⋊#157 | semidirect |
| 243. C22 | Dic3⋊#157 | direct (N × H) |
| 251. C3 | C22×C4⋊#157 | semidirect |
| 255. C2 | C2×Dic3⋊#157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3⋊#157 | 2 |
| C23×C3×#157 | 2 |
| C22×Dic3×C3⋊D3 | 2 |
| C2×Dic3⋊#157 | 2 |
| C22×C4⋊#157 | 3 |
| C22×Dic3⋊C4 | 9 |