Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
628 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 178 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. H(3,𝔽3)×C22⋊C9 | C2 | direct (N × H) |
| 3. C2×C32×C22⋊C9 | C3 | semidirect |
| 4. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 9. C32×C22⋊C9 | C2×C3 | semidirect |
| 10. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 13. C23×H(3,𝔽3) | C9 | semidirect |
| 27. C22×H(3,𝔽3) | C2×C9 | semidirect |
| 36. C23×C32 | C3×C9 | semidirect |
| 39. C2×C22⋊C9 | H(3,𝔽3) | direct (N × H) |
| 45. C2×H(3,𝔽3) | C22⋊C9 | direct (N × H) |
| 59. C22×C32 | C2×C3×C9 | semidirect |
| 62. C22⋊C9 | C2×H(3,𝔽3) | direct (N × H) |
| 64. H(3,𝔽3) | C2×C22⋊C9 | direct (N × H) |
| 82. C2×C32 | C3×C22⋊C9 | semidirect |
| 100. C32 | C2×C3×C22⋊C9 | semidirect |
| 104. C23 | C9×H(3,𝔽3) | semidirect |
| 119. C22 | C2×C9×H(3,𝔽3) | semidirect |
| 126. C2 | H(3,𝔽3)×C22⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×C22⋊C9 | 2 |
| C23×C3×H(3,𝔽3) | 3 |
| C2×C32×C22⋊C9 | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×C9×H(3,𝔽3) | 4 |