Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1223 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 1223 conjugacy classes of subgroups — too many to draw. Only its 196 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. C2×C3⋊D3×H(3,𝔽3) | C2 | semidirect |
| 2. C2×C3×D3×H(3,𝔽3) | C2 | semidirect |
| 3. D32×H(3,𝔽3) | C2 | direct (N × H) |
| 4. C2×C32×D32 | C3 | semidirect |
| 6. C2×C32×H(3,𝔽3) | C22 | semidirect |
| 7. C3⋊D3×H(3,𝔽3) | C22 | semidirect |
| 8. C3×D3×H(3,𝔽3) | C22 | semidirect |
| 9. C2×C32×C3⋊D3 | C2×C3 | semidirect |
| 10. C2×C33×D3 | C2×C3 | semidirect |
| 11. C32×D32 | C2×C3 | semidirect |
| 17. C2×D3×H(3,𝔽3) | D3 | direct (N × H) |
| 18. C32×H(3,𝔽3) | C23 | semidirect |
| 23. C2×C34 | C22×C3 | semidirect |
| 24. C32×C3⋊D3 | C22×C3 | semidirect |
| 25. C33×D3 | C22×C3 | semidirect |
| 30. C2×C3×H(3,𝔽3) | C2×D3 | semidirect |
| 34. D3×H(3,𝔽3) | C2×D3 | direct (N × H) |
| 44. C2×C32×D3 | C3×D3 | semidirect |
| 52. C34 | C23×C3 | semidirect |
| 56. C3×H(3,𝔽3) | C22×D3 | semidirect |
| 60. C2×D32 | H(3,𝔽3) | direct (N × H) |
| 68. C2×C33 | C2×C3×D3 | semidirect |
| 77. C32×D3 | C2×C3×D3 | semidirect |
| 85. C2×H(3,𝔽3) | D32 | direct (N × H) |
| 93. C2×C3⋊D3 | C2×H(3,𝔽3) | semidirect |
| 103. C2×C3×D3 | C2×H(3,𝔽3) | semidirect |
| 105. D32 | C2×H(3,𝔽3) | direct (N × H) |
| 112. C33 | C22×C3×D3 | semidirect |
| 117. H(3,𝔽3) | C2×D32 | direct (N × H) |
| 140. C2×C32 | C22×H(3,𝔽3) | semidirect |
| 141. C2×C32 | C3×D32 | semidirect |
| 143. C3⋊D3 | C22×H(3,𝔽3) | semidirect |
| 151. C3×D3 | C22×H(3,𝔽3) | semidirect |
| 165. C2×D3 | D3×H(3,𝔽3) | direct (N × H) |
| 179. C32 | C23×H(3,𝔽3) | semidirect |
| 180. C32 | C2×C3×D32 | semidirect |
| 196. C2×C3 | C2×D3×H(3,𝔽3) | semidirect |
| 200. D3 | C2×D3×H(3,𝔽3) | direct (N × H) |
| 210. C3 | C22×D3×H(3,𝔽3) | semidirect |
| 214. C2 | D32×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 |
|---|---|
| C2×C3⋊D3×H(3,𝔽3) | 2 |
| C2×C3×D3×H(3,𝔽3) | 2 |
| D32×H(3,𝔽3) | 2 |
| C2×C32×D32 | 3 |
| C22×D3×H(3,𝔽3) | 3 |