Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1876 conjugacy classes of subgroups; only the 629 normal subgroups are shown.
This group has 1876 conjugacy classes of subgroups — too many to draw. Only its 629 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 |
|---|---|---|
| 96. C33 | #400 | semidirect |
| 132. C32 | #4985 | semidirect |
| 161. C3 | #10592684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C4⋊C4 | 2 |
| C2×#88857 | 2 |
| #11722201 | 2 |
| #10592684 | 3 |