Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1512 conjugacy classes of subgroups; only the 515 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 515 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 |
|---|---|---|
| 48. C33×C4 | Q16 | semidirect |
| 86. C32×C4 | #216 | semidirect |
| 95. C33 | #462 | semidirect |
| 124. C3×C4 | #3756 | semidirect |
| 128. C32 | #5031 | semidirect |
| 148. C4 | #88863 | semidirect |
| 151. C3 | #10592730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×Q8 | 2 |
| C2×#88863 | 2 |
| #11723910 | 2 |
| #11722180 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| #10592730 | 3 |