Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
275 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 46 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. C9×C3⋊S4 | C3 | semidirect |
| 5. (C3⋊S4)⋊C9 | C3 | semidirect |
| 7. C22×C32×C9 | D3 | semidirect |
| 11. C3×C9×A4 | C2×C3 | semidirect |
| 15. (C3×A4)⋊C9 | C2×C3 | semidirect |
| 19. (C3⋊S4)⋊C3 | C9 | direct (N × H) |
| 42. C22⋊H(3,𝔽3) | C2×C9 | semidirect |
| 55. C32×C9 | S4 | semidirect |
| 59. C3⋊S4 | C3×C9 | semidirect |
| 83. C22×C32 | D3×C9 | semidirect |
| 93. C3×A4 | C2×C3×C9 | semidirect |
| 101. C22×C9 | (C3⋊D3)⋊C3 | semidirect |
| 163. C32 | C9×S4 | semidirect |
| 169. C9 | (C3⋊S4)⋊C3 | direct (N × H) |
| 181. 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 |
| C9×C3⋊S4 | 3 |
| C3×(C3⋊S4)⋊C3 | 3 |
| C3×C9×#67 | 3 |
| (C3⋊S4)⋊C9 | 3 |
| C9×(C3⋊D3)⋊C3 | 4 |