Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
572 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 162 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×#92262 | C2 | direct (N × H) |
| 3. C22×C9×C3⋊D3 | C3 | semidirect |
| 6. C22×(C3⋊D3)⋊C9 | C3 | semidirect |
| 7. C2×C9⋊H(3,𝔽3) | C22 | semidirect |
| 8. #92262 | C22 | direct (N × H) |
| 10. C22×C3×3−1+2 | D3 | semidirect |
| 12. C22×C32×C9 | C2×C3 | semidirect |
| 13. C2×C9×C3⋊D3 | C2×C3 | semidirect |
| 18. C22×C32⋊C9 | C2×C3 | semidirect |
| 19. C2×(C3⋊D3)⋊C9 | C2×C3 | semidirect |
| 20. C9⋊H(3,𝔽3) | C23 | semidirect |
| 29. C2×C3×3−1+2 | C2×D3 | semidirect |
| 31. C2×C32×C9 | C22×C3 | semidirect |
| 32. C9×C3⋊D3 | C22×C3 | semidirect |
| 37. C2×C32⋊C9 | C22×C3 | semidirect |
| 38. (C3⋊D3)⋊C9 | C22×C3 | semidirect |
| 62. C3×3−1+2 | C22×D3 | semidirect |
| 64. C32×C9 | C23×C3 | semidirect |
| 67. C32⋊C9 | C23×C3 | semidirect |
| 69. C22×C3⋊D3 | 3−1+2 | semidirect |
| 107. C22×C32 | C2×3−1+2 | semidirect |
| 109. C2×C3⋊D3 | C2×3−1+2 | semidirect |
| 119. C22×C9 | (C3⋊D3)⋊C3 | semidirect |
| 149. C2×C32 | C22×3−1+2 | semidirect |
| 151. C3⋊D3 | C22×3−1+2 | semidirect |
| 161. C2×C9 | C2×(C3⋊D3)⋊C3 | semidirect |
| 182. C32 | C23×3−1+2 | semidirect |
| 188. C9 | C22×(C3⋊D3)⋊C3 | semidirect |
| 202. C22 | #92262 | direct (N × H) |
| 211. C2 | C2×#92262 | 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×#92262 | 2 |
| C22×C9×C3⋊D3 | 3 |
| C22×D3×3−1+2 | 3 |
| C22×C3×(C3⋊D3)⋊C3 | 3 |
| C22×(C3⋊D3)⋊C9 | 3 |