Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
288 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 40 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×C32×D9 | C3 | semidirect |
| 4. C3×A4×D9 | C3 | semidirect |
| 6. C22×C32×C9 | C2×C3 | semidirect |
| 10. C3×C9×A4 | C2×C3 | semidirect |
| 24. C32×D9 | A4 | semidirect |
| 39. C22⋊H(3,𝔽3) | D9 | direct (N × H) |
| 45. C32×C9 | C2×A4 | semidirect |
| 53. C22×D9 | H(3,𝔽3) | semidirect |
| 73. C22×C32 | C3×D9 | semidirect |
| 82. C3×A4 | C3×D9 | semidirect |
| 85. C22×C9 | C2×H(3,𝔽3) | semidirect |
| 122. D9 | C22⋊H(3,𝔽3) | direct (N × H) |
| 143. C32 | A4×D9 | semidirect |
| 148. C9 | C2×C22⋊H(3,𝔽3) | semidirect |
| 164. C22 | D9×H(3,𝔽3) | 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×C32×D9 | 3 |
| D3×C22⋊H(3,𝔽3) | 3 |
| C3×A4×D9 | 3 |
| D9×H(3,𝔽3) | 4 |