Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
533 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 533 conjugacy classes of subgroups — too many to draw. Only its 108 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. C3×#66436 | C2 | semidirect |
| 2. C22×C3×D3×C9 | C3 | semidirect |
| 5. D3×#1094 | C3 | semidirect |
| 6. D3×C9⋊A4 | C3 | semidirect |
| 7. D3×C9×A4 | C3 | semidirect |
| 9. C22×C32×C9 | C2×C3 | semidirect |
| 13. C3×#1094 | C2×C3 | semidirect |
| 19. #66436 | D3 | direct (N × H) |
| 20. C3×C9⋊A4 | C2×C3 | semidirect |
| 21. C3×C9×A4 | C2×C3 | semidirect |
| 40. C3×D3×C9 | A4 | semidirect |
| 50. C22×C3×C9 | C3×D3 | semidirect |
| 62. #1094 | C3×D3 | semidirect |
| 67. C9⋊A4 | C3×D3 | semidirect |
| 71. C9×A4 | C3×D3 | semidirect |
| 82. C32×C9 | C2×A4 | semidirect |
| 157. C3×C9 | D3×A4 | semidirect |
| 162. C22×D3 | #737 | semidirect |
| 193. C22×C3 | C2×#737 | semidirect |
| 226. D3 | #66436 | direct (N × H) |
| 229. C22 | D3×#737 | semidirect |
| 235. C3 | C2×#66436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66436 | 2 |
| C22×C3×D3×C9 | 3 |
| C2×#66436 | 3 |
| D3×C22⋊H(3,𝔽3) | 3 |
| D3×#1094 | 3 |
| D3×C9⋊A4 | 3 |
| D3×C9×A4 | 3 |
| D3×#737 | 4 |