Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
298 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 53 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. H(3,𝔽3)×C22⋊C9 | C2 | semidirect |
| 3. C3⋊D3×C22⋊C9 | C3 | semidirect |
| 5. (C3⋊D3)⋊(C22⋊C9) | C3 | semidirect |
| 11. C32×C22⋊C9 | D3 | semidirect |
| 12. C32×C22⋊C9 | C2×C3 | semidirect |
| 15. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 19. C22×(C3⋊D3)⋊C3 | C9 | semidirect |
| 38. C22×H(3,𝔽3) | C2×C9 | semidirect |
| 59. C22×C3⋊D3 | C3×C9 | semidirect |
| 76. (C3⋊D3)⋊C3 | C22⋊C9 | direct (N × H) |
| 90. C22×C32 | D3×C9 | semidirect |
| 91. C22×C32 | C2×C3×C9 | semidirect |
| 105. C22⋊C9 | (C3⋊D3)⋊C3 | direct (N × H) |
| 110. H(3,𝔽3) | C2×C22⋊C9 | semidirect |
| 139. C3⋊D3 | C3×C22⋊C9 | semidirect |
| 171. C32 | D3×C22⋊C9 | semidirect |
| 172. C32 | C2×C3×C22⋊C9 | semidirect |
| 197. 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 |
|---|---|
| H(3,𝔽3)×C22⋊C9 | 2 |
| C22×C3×(C3⋊D3)⋊C3 | 3 |
| C3⋊D3×C22⋊C9 | 3 |
| C3×D3×C22⋊C9 | 3 |
| (C3⋊D3)⋊(C22⋊C9) | 3 |
| C9×(C3⋊D3)⋊C3 | 4 |