Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
434 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 99 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×C9×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. C9×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. C9×#638 | C3 | semidirect |
| 7. #638⋊C9 | C3 | semidirect |
| 13. C22×C32×C9 | D3 | semidirect |
| 14. C22×C32×C9 | C2×C3 | semidirect |
| 15. C2×C9×C3⋊D3 | C2×C3 | semidirect |
| 18. C9×C3⋊Dic3 | C2×C3 | semidirect |
| 23. C22×C32⋊C9 | C2×C3 | semidirect |
| 24. C2×(C3⋊D3)⋊C9 | C2×C3 | semidirect |
| 25. (C3⋊Dic3)⋊C9 | C2×C3 | semidirect |
| 26. C9×H(3,𝔽3) | D4 | semidirect |
| 30. #638⋊C3 | C9 | direct (N × H) |
| 60. C22×H(3,𝔽3) | C2×C9 | semidirect |
| 72. C2×(C3⋊D3)⋊C3 | C2×C9 | semidirect |
| 77. (C3⋊Dic3)⋊C3 | C2×C9 | semidirect |
| 83. C32×C9 | #67 | semidirect |
| 84. C32×C9 | C3×D4 | semidirect |
| 87. C32⋊C9 | C3×D4 | semidirect |
| 89. #638 | C3×C9 | semidirect |
| 141. C22×C32 | D3×C9 | semidirect |
| 142. C22×C32 | C2×C3×C9 | semidirect |
| 144. C2×C3⋊D3 | C2×C3×C9 | semidirect |
| 149. C3⋊Dic3 | C2×C3×C9 | semidirect |
| 159. C22×C9 | (C3⋊D3)⋊C3 | semidirect |
| 166. H(3,𝔽3) | D4×C9 | semidirect |
| 243. C32 | C9×#67 | semidirect |
| 244. C32 | C3×D4×C9 | semidirect |
| 250. C9 | #638⋊C3 | direct (N × H) |
| 271. C22 | C9×(C3⋊D3)⋊C3 | semidirect |
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×C9×(C3⋊D3)⋊C3 | 2 |
| C9×(C3⋊Dic3)⋊C3 | 2 |
| C9×#638 | 3 |
| C3×#638⋊C3 | 3 |
| C3×C9×#67 | 3 |
| #638⋊C9 | 3 |