Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
648 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 160 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. #10593735 | C3 | direct (N × H) |
| 7. C33×C42 | C4 | semidirect |
| 8. C3×C4×C3⋊Dic3 | C4 | semidirect |
| 25. C32×C42 | C3×C4 | semidirect |
| 26. C4×C3⋊Dic3 | C3×C4 | semidirect |
| 32. C33×C4 | C4⋊C4 | semidirect |
| 33. C3×C3⋊Dic3 | C4⋊C4 | semidirect |
| 60. C3×C42 | #157 | semidirect |
| 72. C32×C4 | C3×C4⋊C4 | semidirect |
| 73. C3⋊Dic3 | C3×C4⋊C4 | semidirect |
| 77. C33 | #384 | semidirect |
| 101. C42 | C3×#157 | semidirect |
| 113. C3×C4 | C4⋊#157 | semidirect |
| 117. C32 | C3×#384 | semidirect |
| 136. C4 | C3×C4⋊#157 | semidirect |
| 139. C3 | #10593735 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊#157 | 2 |
| C3×C42×C3⋊D3 | 2 |
| #10593735 | 3 |
| C3×#384 | 9 |