Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 2. #11720572 | C2 | semidirect |
| 3. #11720571 | C2 | semidirect |
| 7. C2×C3×D4×C9 | C4 | semidirect |
| 10. C3×C9×C4⋊C4 | C4 | semidirect |
| 42. C2×D4×C9 | Dic3 | semidirect |
| 45. C9×C4⋊C4 | Dic3 | semidirect |
| 101. C2×C3×D4 | Dic9 | semidirect |
| 107. C3×C4⋊C4 | Dic9 | semidirect |
| 140. C3×C9 | #327 | semidirect |
| 180. C2×D4 | C3⋊Dic9 | semidirect |
| 184. C4⋊C4 | C3⋊Dic9 | semidirect |
| 211. C9 | #4537 | semidirect |
| 249. C3 | #10588214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#121 | 2 |
| #11720572 | 2 |
| #11720571 | 2 |
| #10589403 | 3 |
| #10588214 | 3 |