Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
584 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. C3×C32⋊(C22⋊C9) | C2 | semidirect |
| 3. C3×D3×C22⋊C9 | C3 | semidirect |
| 9. C32×C22⋊C9 | C2×C3 | semidirect |
| 12. C32⋊(C22⋊C9) | D3 | direct (N × H) |
| 17. C22×C32×D3 | C9 | semidirect |
| 34. C22×C33 | C2×C9 | semidirect |
| 48. C3×C22⋊C9 | C3×D3 | semidirect |
| 80. C32×D3 | C22⋊C9 | semidirect |
| 104. C22×C32 | D3×C9 | semidirect |
| 125. C33 | C2×C22⋊C9 | semidirect |
| 136. C22×D3 | C32⋊C9 | semidirect |
| 184. C22×C3 | C2×C32⋊C9 | semidirect |
| 202. C32 | D3×C22⋊C9 | semidirect |
| 228. D3 | C32⋊(C22⋊C9) | direct (N × H) |
| 231. C22 | D3×C32⋊C9 | semidirect |
| 237. C3 | C2×C32⋊(C22⋊C9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊(C22⋊C9) | 2 |
| C22×C33×D3 | 3 |
| C3×D3×C22⋊C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| D3×C32⋊C9 | 4 |