Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
496 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 2. C4×C9×H(3,𝔽3) | C2 | semidirect |
| 3. C9×#1084 | C2 | semidirect |
| 7. C9×#272 | C4 | direct (N × H) |
| 11. C32×C4×C9 | D3 | semidirect |
| 15. C9×H(3,𝔽3) | C2×C4 | semidirect |
| 18. C4×#272 | C9 | direct (N × H) |
| 32. C4×H(3,𝔽3) | C2×C9 | semidirect |
| 37. #1084 | C2×C9 | semidirect |
| 40. C32×C9 | C4×D3 | semidirect |
| 55. #272 | C4×C9 | direct (N × H) |
| 65. C32×C4 | D3×C9 | semidirect |
| 73. C4×C9 | #272 | direct (N × H) |
| 76. H(3,𝔽3) | C2×C4×C9 | semidirect |
| 112. C32 | C4×D3×C9 | semidirect |
| 115. C9 | C4×#272 | direct (N × H) |
| 128. C4 | C9×#272 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#272 | 2 |
| C4×C9×H(3,𝔽3) | 2 |
| C9×#1084 | 2 |
| C3×C4×#272 | 3 |
| C3×C4×D3×C9 | 3 |