Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2044 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 2044 conjugacy classes of subgroups — too many to draw. Only its 459 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 |
|---|---|---|
| 1. C33×2−1+4 | C2 | semidirect |
| 2. #11723990 | C2 | semidirect |
| 3. #11723988 | C2 | semidirect |
| 4. #11722207 | C2 | semidirect |
| 5. #11722206 | C2 | semidirect |
| 18. C32×2−1+4 | D3 | semidirect |
| 57. C3×2−1+4 | C3⋊D3 | semidirect |
| 100. 2−1+4 | C3⋊(C3⋊D3) | semidirect |
| 105. C33 | #454 | semidirect |
| 143. C32 | #5245 | semidirect |
| 170. C3 | #10592944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×2−1+4 | 2 |
| #11723990 | 2 |
| #11723988 | 2 |
| #11722207 | 2 |
| #11722206 | 2 |
| #10592944 | 3 |