Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
152 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 9. C3⋊(C9⋊C16) | C4 | semidirect |
| 85. C3×C9 | #365 | semidirect |
| 122. C9 | #4494 | semidirect |
| 139. C3 | #10588164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720534 | 2 |
| C9×#817 | 2 |
| C3×#63372 | 2 |
| #10589138 | 3 |
| #10588164 | 3 |