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×#106 | C2 | semidirect |
| 4. #11722187 | C2 | semidirect |
| 5. #11722177 | C2 | semidirect |
| 14. C8×C3⋊(C3⋊D3) | C4 | semidirect |
| 17. C32×#106 | D3 | semidirect |
| 48. C3×#106 | C3⋊D3 | semidirect |
| 84. #106 | C3⋊(C3⋊D3) | semidirect |
| 85. C33 | #427 | semidirect |
| 114. C32 | #4860 | semidirect |
| 135. C3 | #10592559 | 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×#106 | 2 |
| #11722187 | 2 |
| #11722177 | 2 |
| #10592559 | 3 |