Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
288 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 45 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. C9×C22⋊H(3,𝔽3) | C2 | semidirect |
| 2. C22×C9×C3⋊D3 | C3 | semidirect |
| 5. (C3⋊D3)⋊(C22⋊C9) | C3 | semidirect |
| 7. C22×C32×C9 | C2×C3 | semidirect |
| 12. C3×C9×A4 | D3 | semidirect |
| 13. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 22. (C3⋊D3)⋊A4 | C9 | direct (N × H) |
| 26. C9×C3⋊D3 | A4 | semidirect |
| 44. C22⋊H(3,𝔽3) | C2×C9 | semidirect |
| 54. C32×C9 | C2×A4 | semidirect |
| 58. C22×C3⋊D3 | C3×C9 | semidirect |
| 83. C22×C32 | C2×C3×C9 | semidirect |
| 96. C3×A4 | D3×C9 | semidirect |
| 101. C22×C9 | (C3⋊D3)⋊C3 | semidirect |
| 130. C3⋊D3 | C9×A4 | semidirect |
| 164. C32 | C2×C9×A4 | semidirect |
| 170. C9 | (C3⋊D3)⋊A4 | direct (N × H) |
| 186. C22 | C9×(C3⋊D3)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C22⋊H(3,𝔽3) | 2 |
| C22×C9×C3⋊D3 | 3 |
| C3×(C3⋊D3)⋊A4 | 3 |
| D3×C9×A4 | 3 |
| (C3⋊D3)⋊(C22⋊C9) | 3 |
| C9×(C3⋊D3)⋊C3 | 4 |