Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
250 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 44 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. #11757775 | C2 | semidirect |
| 2. C3⋊D3×C22⋊C9 | C3 | semidirect |
| 5. C22×(C3⋊D3)⋊C9 | C3 | semidirect |
| 6. (C3⋊D3)⋊(C22⋊C9) | C3 | semidirect |
| 9. C32×C22⋊C9 | C2×C3 | semidirect |
| 11. C3×C9×A4 | D3 | semidirect |
| 12. C22×C32⋊C9 | C2×C3 | semidirect |
| 15. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 24. (C3⋊D3)⋊A4 | C9 | semidirect |
| 34. (C3⋊D3)⋊C9 | A4 | semidirect |
| 45. C22⋊H(3,𝔽3) | C2×C9 | semidirect |
| 64. C32⋊C9 | C2×A4 | semidirect |
| 65. C22×C3⋊D3 | C3×C9 | semidirect |
| 89. C22×C32 | C2×C3×C9 | semidirect |
| 102. C3×A4 | D3×C9 | semidirect |
| 111. C22⋊C9 | (C3⋊D3)⋊C3 | semidirect |
| 140. C3⋊D3 | C9×A4 | semidirect |
| 174. C32 | C2×C9×A4 | semidirect |
| 198. 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 |
|---|---|
| #11757775 | 2 |
| C3⋊D3×C22⋊C9 | 3 |
| C3×(C3⋊D3)⋊A4 | 3 |
| D3×C9×A4 | 3 |
| C22×(C3⋊D3)⋊C9 | 3 |
| (C3⋊D3)⋊(C22⋊C9) | 3 |
| C9×(C3⋊D3)⋊C3 | 4 |