Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1568 conjugacy classes of subgroups; only the 405 normal subgroups are shown.
This group has 1568 conjugacy classes of subgroups — too many to draw. Only its 405 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. C2×#88853 | C2 | semidirect |
| 4. C4×#6308 | C2 | semidirect |
| 5. C33×C4⋊C8 | C2 | semidirect |
| 7. #11722186 | C2 | semidirect |
| 26. C32×C4⋊C8 | D3 | semidirect |
| 73. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 124. C4⋊C8 | C3⋊(C3⋊D3) | semidirect |
| 127. C33 | #464 | semidirect |
| 171. C32 | #4845 | semidirect |
| 202. C3 | #10592544 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88853 | 2 |
| C2×#88851 | 2 |
| #11723916 | 2 |
| C4×#6308 | 2 |
| C33×C4⋊C8 | 2 |
| #11722191 | 2 |
| #11722186 | 2 |
| #10592544 | 3 |