Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1096 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 1096 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#88994 | C2 | semidirect |
| 3. C2×C4⋊(C3⋊#157) | C2 | semidirect |
| 4. C2×C4×C3⋊#157 | C2 | semidirect |
| 9. C2×C33×D4 | C4 | semidirect |
| 10. C2×C3×#638 | C4 | semidirect |
| 13. C2×C3×C4⋊(C3⋊D3) | C4 | semidirect |
| 34. C2×C3⋊#157 | D4 | semidirect |
| 49. C2×C32×D4 | Dic3 | semidirect |
| 50. C2×#638 | Dic3 | semidirect |
| 53. C2×C4⋊(C3⋊D3) | Dic3 | semidirect |
| 77. C33×C4 | C22⋊C4 | semidirect |
| 78. C3×C3⋊Dic3 | C22⋊C4 | semidirect |
| 136. C2×C3×D4 | #157 | semidirect |
| 179. C32×C4 | #217 | semidirect |
| 180. C3⋊Dic3 | #217 | semidirect |
| 186. C33 | #390 | semidirect |
| 245. C2×D4 | C3⋊#157 | semidirect |
| 282. C3×C4 | C22⋊#157 | semidirect |
| 288. C32 | #5221 | semidirect |
| 340. C4 | #88994 | semidirect |
| 343. C3 | #10593827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C3⋊D3 | 2 |
| C2×#88994 | 2 |
| C2×C4⋊(C3⋊#157) | 2 |
| C2×C4×C3⋊#157 | 2 |
| #10593827 | 3 |
| #5221 | 9 |