Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
340 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 7. C22×C3×C4×C9 | C4 | semidirect |
| 10. C3×C9×C22⋊C4 | C4 | semidirect |
| 38. C22×C4×C9 | Dic3 | semidirect |
| 41. C9×C22⋊C4 | Dic3 | semidirect |
| 84. C22×C3×C4 | Dic9 | semidirect |
| 90. C3×C22⋊C4 | Dic9 | semidirect |
| 117. C3×C9 | #352 | semidirect |
| 145. C22×C4 | C3⋊Dic9 | semidirect |
| 150. C22⋊C4 | C3⋊Dic9 | semidirect |
| 170. C9 | #4539 | semidirect |
| 197. C3 | #10588216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#123 | 2 |
| #11720577 | 2 |
| #11720575 | 2 |
| #10589405 | 3 |
| #10588216 | 3 |