Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1596 conjugacy classes of subgroups; only the 353 normal subgroups are shown.
This group has 1596 conjugacy classes of subgroups — too many to draw. Only its 353 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×#88863 | C2 | semidirect |
| 5. C33×#103 | C2 | semidirect |
| 6. #11722186 | C2 | semidirect |
| 7. #11722177 | C2 | semidirect |
| 26. C32×#103 | D3 | semidirect |
| 61. C2×C3⋊(C3⋊D3) | Q16 | semidirect |
| 73. C3×#103 | C3⋊D3 | semidirect |
| 126. #103 | C3⋊(C3⋊D3) | semidirect |
| 127. C33 | #467 | semidirect |
| 171. C32 | #4813 | semidirect |
| 202. C3 | #10592512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723987 | 2 |
| C2×#88863 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| #11723938 | 2 |
| C33×#103 | 2 |
| #11722186 | 2 |
| #11722177 | 2 |
| #10592512 | 3 |