Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3276 conjugacy classes of subgroups; only the 971 normal subgroups are shown.
This group has 3276 conjugacy classes of subgroups — too many to draw. Only its 971 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×#88857 | C2 | semidirect |
| 5. #11722201 | C2 | semidirect |
| 15. #88864 | C4 | semidirect |
| 38. C2×C3⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 54. C22×C33 | C4⋊C4 | semidirect |
| 107. C22×C32 | Dic3⋊C4 | semidirect |
| 122. C33 | #385 | semidirect |
| 160. C22×C3 | #3750 | semidirect |
| 170. C32 | #5210 | semidirect |
| 198. C22 | #88857 | semidirect |
| 208. C3 | #10592909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C33×C4 | 2 |
| C2×#88864 | 2 |
| C2×#88857 | 2 |
| #11722201 | 2 |
| #10592909 | 3 |