Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
710 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 227 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 |
|---|---|---|
| 6. C22×C3×C4×C9 | C4 | semidirect |
| 10. #88551 | C4 | semidirect |
| 34. C22×C4×C9 | Dic3 | semidirect |
| 84. C22×C3×C4 | Dic9 | semidirect |
| 120. C3×C9 | #342 | semidirect |
| 155. C22×C4 | C3⋊Dic9 | semidirect |
| 184. C9 | #4526 | semidirect |
| 219. C3 | #10588203 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×C22⋊C4 | 2 |
| C2×#88551 | 2 |
| #10589392 | 3 |
| #10588203 | 3 |