Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
698 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 182 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. C22×C9×H(3,𝔽3) | C2 | semidirect |
| 2. C2×D9×H(3,𝔽3) | C2 | direct (N × H) |
| 4. C22×C32×D9 | C3 | semidirect |
| 5. C2×C9×H(3,𝔽3) | C22 | semidirect |
| 6. D9×H(3,𝔽3) | C22 | direct (N × H) |
| 8. C22×C32×C9 | C2×C3 | semidirect |
| 10. C2×C32×D9 | C2×C3 | semidirect |
| 12. C9×H(3,𝔽3) | C23 | semidirect |
| 18. C2×C32×C9 | C22×C3 | semidirect |
| 20. C32×D9 | C22×C3 | semidirect |
| 26. C22×H(3,𝔽3) | D9 | direct (N × H) |
| 34. C32×C9 | C23×C3 | semidirect |
| 39. C22×D9 | H(3,𝔽3) | direct (N × H) |
| 44. C2×H(3,𝔽3) | C2×D9 | direct (N × H) |
| 55. C22×C32 | C3×D9 | semidirect |
| 61. C22×C9 | C2×H(3,𝔽3) | semidirect |
| 62. C2×D9 | C2×H(3,𝔽3) | direct (N × H) |
| 65. H(3,𝔽3) | C22×D9 | direct (N × H) |
| 77. C2×C32 | C2×C3×D9 | semidirect |
| 83. C2×C9 | C22×H(3,𝔽3) | semidirect |
| 84. D9 | C22×H(3,𝔽3) | direct (N × H) |
| 96. C32 | C22×C3×D9 | semidirect |
| 100. C9 | C23×H(3,𝔽3) | semidirect |
| 111. C22 | D9×H(3,𝔽3) | direct (N × H) |
| 118. C2 | C2×D9×H(3,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×H(3,𝔽3) | 2 |
| C2×D9×H(3,𝔽3) | 2 |
| C22×D3×H(3,𝔽3) | 3 |
| C22×C32×D9 | 3 |