Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1596 conjugacy classes of subgroups; only the 419 normal subgroups are shown.
This group has 1596 conjugacy classes of subgroups — too many to draw. Only its 419 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 |
|---|---|---|
| 3. C33×#107 | C2 | semidirect |
| 4. #11722188 | C2 | semidirect |
| 5. #11722178 | C2 | semidirect |
| 14. C8×C3⋊(C3⋊D3) | C4 | semidirect |
| 17. C32×#107 | D3 | semidirect |
| 49. C3×#107 | C3⋊D3 | semidirect |
| 86. #107 | C3⋊(C3⋊D3) | semidirect |
| 88. C33 | #427 | semidirect |
| 119. C32 | #4880 | semidirect |
| 142. C3 | #10592579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊(C3⋊D3) | 2 |
| #11723933 | 2 |
| C33×#107 | 2 |
| #11722188 | 2 |
| #11722178 | 2 |
| #10592579 | 3 |