Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1320 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 210 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×C33×C9 | C2 | semidirect |
| 2. C2×C3×C9×C3⋊D3 | C2 | semidirect |
| 3. C3×C9×C3⋊Dic3 | C2 | semidirect |
| 5. C9×#638 | C3 | direct (N × H) |
| 15. C22×C32×C9 | D3 | semidirect |
| 16. C22×C32×C9 | C2×C3 | semidirect |
| 17. C2×C9×C3⋊D3 | C2×C3 | semidirect |
| 19. C9×C3⋊Dic3 | C2×C3 | semidirect |
| 21. C33×C9 | D4 | semidirect |
| 22. C3×#638 | C9 | direct (N × H) |
| 42. C22×C33 | C2×C9 | semidirect |
| 45. C2×C3×C3⋊D3 | C2×C9 | semidirect |
| 48. C3×C3⋊Dic3 | C2×C9 | semidirect |
| 56. C22×C3×C9 | C3×D3 | semidirect |
| 57. C22×C3×C9 | C3⋊D3 | semidirect |
| 64. C32×C9 | #67 | semidirect |
| 65. C32×C9 | C3×D4 | semidirect |
| 67. #638 | C3×C9 | direct (N × H) |
| 104. C22×C32 | D3×C9 | semidirect |
| 105. C22×C32 | C2×C3×C9 | semidirect |
| 108. C2×C3⋊D3 | C2×C3×C9 | semidirect |
| 112. C3⋊Dic3 | C2×C3×C9 | semidirect |
| 117. C22×C9 | C3×C3⋊D3 | semidirect |
| 121. C33 | D4×C9 | semidirect |
| 128. C3×C9 | C3×#67 | semidirect |
| 129. C3×C9 | #638 | direct (N × H) |
| 164. C22×C3 | C3×D3×C9 | semidirect |
| 165. C22×C3 | C9×C3⋊D3 | semidirect |
| 176. C32 | C9×#67 | semidirect |
| 177. C32 | C3×D4×C9 | semidirect |
| 181. C9 | C3×#638 | direct (N × H) |
| 197. C22 | C3×C9×C3⋊D3 | semidirect |
| 201. C3 | C3×C9×#67 | semidirect |
| 202. C3 | C9×#638 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×C9 | 2 |
| C2×C3×C9×C3⋊D3 | 2 |
| C3×C9×C3⋊Dic3 | 2 |
| C32×#638 | 3 |
| C9×#638 | 3 |
| C3×C9×#67 | 3 |