Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1160 conjugacy classes of subgroups; only the 496 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 496 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 | direct (N × H) |
| 2. C23×C32×C9 | C3 | semidirect |
| 4. C2×C3×#1094 | C3 | semidirect |
| 5. C2×#66436 | C3 | direct (N × H) |
| 6. C2×C3×C9⋊A4 | C3 | semidirect |
| 7. C2×C3×C9×A4 | C3 | semidirect |
| 11. C22×C32×C9 | C2×C3 | semidirect |
| 13. C3×#1094 | C2×C3 | semidirect |
| 14. #66436 | C2×C3 | direct (N × H) |
| 15. C3×C9⋊A4 | C2×C3 | semidirect |
| 16. C3×C9×A4 | C2×C3 | semidirect |
| 22. C23×C3×C9 | C32 | semidirect |
| 24. C2×#1094 | C32 | semidirect |
| 26. C2×C9⋊A4 | C32 | semidirect |
| 27. C2×C9×A4 | C32 | semidirect |
| 35. C2×C32×C9 | A4 | semidirect |
| 48. C22×C3×C9 | C2×C32 | semidirect |
| 50. #1094 | C2×C32 | semidirect |
| 52. C9⋊A4 | C2×C32 | semidirect |
| 53. C9×A4 | C2×C32 | semidirect |
| 59. C32×C9 | C2×A4 | semidirect |
| 85. C2×C3×C9 | C3×A4 | semidirect |
| 113. C3×C9 | C2×C3×A4 | semidirect |
| 115. C23×C3 | #737 | semidirect |
| 143. C22×C3 | C2×#737 | semidirect |
| 154. C23 | C3×#737 | semidirect |
| 163. C2×C3 | #66436 | direct (N × H) |
| 167. C22 | C2×C3×#737 | semidirect |
| 170. C3 | C2×#66436 | direct (N × H) |
| 174. C2 | C3×#66436 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66436 | 2 |
| C23×C32×C9 | 3 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×C3×#1094 | 3 |
| C2×#66436 | 3 |
| C2×C3×C9⋊A4 | 3 |
| C2×C3×C9×A4 | 3 |
| C2×C3×#737 | 4 |