Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
678 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
| 8. C9⋊#272 | C4 | direct (N × H) |
| 12. C32×C4×C9 | D3 | semidirect |
| 16. C4×C32⋊C9 | D3 | semidirect |
| 18. C9×H(3,𝔽3) | C2×C4 | semidirect |
| 37. C4×H(3,𝔽3) | D9 | semidirect |
| 47. C32×C9 | C4×D3 | semidirect |
| 48. C32⋊C9 | C4×D3 | semidirect |
| 70. C32×C4 | C3⋊D9 | semidirect |
| 79. C4×C9 | #272 | semidirect |
| 83. H(3,𝔽3) | C4×D9 | semidirect |
| 115. C32 | C4×C3⋊D9 | semidirect |
| 119. C9 | C4×#272 | semidirect |
| 130. 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 |
| C4×C3⋊#272 | 3 |
| C3×C4×C3⋊D9 | 3 |
| C4×#4181 | 3 |