Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1548 conjugacy classes of subgroups; only the 714 normal subgroups are shown.
This group has 1548 conjugacy classes of subgroups — too many to draw. Only its 714 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 |
|---|---|---|
| 4. C3×#4935 | C3 | direct (N × H) |
| 7. C33×C42 | C4 | semidirect |
| 20. #4935 | C32 | direct (N × H) |
| 28. C32×C42 | Dic3 | semidirect |
| 29. C32×C42 | C3×C4 | semidirect |
| 34. C33×C4 | C4⋊C4 | semidirect |
| 66. C3×C42 | C3×Dic3 | semidirect |
| 67. C3×C42 | C32×C4 | semidirect |
| 80. C32×C4 | C4⋊Dic3 | semidirect |
| 81. C32×C4 | C3×C4⋊C4 | semidirect |
| 85. C33 | #384 | semidirect |
| 112. C42 | C32×Dic3 | semidirect |
| 124. C3×C4 | C3×C4⋊Dic3 | semidirect |
| 125. C3×C4 | C32×C4⋊C4 | semidirect |
| 128. C32 | #4935 | direct (N × H) |
| 129. C32 | C3×#384 | semidirect |
| 148. C4 | C32×C4⋊Dic3 | semidirect |
| 150. C3 | C3×#4935 | direct (N × H) |
| 151. C3 | C32×#384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C42 | 2 |
| C2×C32×C4⋊Dic3 | 2 |
| C32×#384 | 3 |
| C3×#4935 | 3 |