Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
432 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 35. C33×C4 | Q16 | semidirect |
| 37. C3×C3⋊Dic3 | Q16 | semidirect |
| 78. C32×C4 | Dic12 | semidirect |
| 80. C3⋊Dic3 | Dic12 | semidirect |
| 90. C33 | #494 | semidirect |
| 128. C3×C4 | #3776 | semidirect |
| 136. C32 | #4699 | semidirect |
| 156. C4 | #88943 | semidirect |
| 159. C3 | #10593450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88943 | 2 |
| C4⋊#6296 | 2 |
| C3×C4×#622 | 2 |
| #10593450 | 3 |
| #4699 | 9 |