Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1372 conjugacy classes of subgroups; only the 623 normal subgroups are shown.
This group has 1372 conjugacy classes of subgroups — too many to draw. Only its 623 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 |
|---|---|---|
| 8. C33×M16 | C4 | semidirect |
| 13. #88855 | C4 | semidirect |
| 33. C32×M16 | Dic3 | semidirect |
| 73. C3×M16 | C3⋊Dic3 | semidirect |
| 93. C33 | #343 | semidirect |
| 115. M16 | C3⋊(C3⋊Dic3) | semidirect |
| 130. C32 | #4554 | semidirect |
| 157. C3 | #10589420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| C2×#88855 | 2 |
| #10589420 | 3 |