Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
513 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 513 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×#66440 | C2 | semidirect |
| 2. C22×D3×3−1+2 | C3 | semidirect |
| 5. D3×#1094 | C3 | semidirect |
| 6. C3×D3×C22⋊C9 | C3 | semidirect |
| 7. D3×C9⋊A4 | C3 | semidirect |
| 8. D3×C9×A4 | C3 | semidirect |
| 10. C22×C3×3−1+2 | C2×C3 | semidirect |
| 14. C3×#1094 | C2×C3 | semidirect |
| 15. C32×C22⋊C9 | C2×C3 | semidirect |
| 22. #66440 | D3 | direct (N × H) |
| 23. C3×C9⋊A4 | C2×C3 | semidirect |
| 24. C3×C9×A4 | C2×C3 | semidirect |
| 43. D3×3−1+2 | A4 | semidirect |
| 55. C22×3−1+2 | C3×D3 | semidirect |
| 64. #1094 | C3×D3 | semidirect |
| 68. C3×C22⋊C9 | C3×D3 | semidirect |
| 76. C9⋊A4 | C3×D3 | semidirect |
| 81. C9×A4 | C3×D3 | semidirect |
| 91. C3×3−1+2 | C2×A4 | semidirect |
| 161. 3−1+2 | D3×A4 | semidirect |
| 180. C22×D3 | #737 | semidirect |
| 209. C22×C3 | C2×#737 | semidirect |
| 244. D3 | #66440 | direct (N × H) |
| 247. C22 | D3×#737 | semidirect |
| 253. C3 | C2×#66440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66440 | 2 |
| C22×D3×3−1+2 | 3 |
| C2×#66440 | 3 |
| D3×C22⋊H(3,𝔽3) | 3 |
| D3×#1094 | 3 |
| C3×D3×C22⋊C9 | 3 |
| D3×C9⋊A4 | 3 |
| D3×C9×A4 | 3 |
| D3×#737 | 4 |