Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
386 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 72 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×C3×#732 | C2 | semidirect |
| 2. C2×D3×#732 | C2 | semidirect |
| 3. Dic3×#732 | C2 | semidirect |
| 4. #67×H(3,𝔽3) | C3 | semidirect |
| 5. C3×C9×#67 | C3 | semidirect |
| 10. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 11. C22×C32×C9 | C2×C3 | semidirect |
| 12. C2×D3×H(3,𝔽3) | C2×C3 | semidirect |
| 13. C2×C3×D3×C9 | C2×C3 | semidirect |
| 14. Dic3×H(3,𝔽3) | C2×C3 | semidirect |
| 15. C3×C9×Dic3 | C2×C3 | semidirect |
| 19. C22×#732 | D3 | semidirect |
| 21. C3×#732 | D4 | semidirect |
| 49. C22×H(3,𝔽3) | C3×D3 | semidirect |
| 54. C22×C3×C9 | C3×D3 | semidirect |
| 59. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 60. C32×C9 | C3×D4 | semidirect |
| 63. #732 | #67 | direct (N × H) |
| 120. H(3,𝔽3) | C3×#67 | semidirect |
| 124. C3×C9 | C3×#67 | semidirect |
| 128. #67 | #732 | direct (N × H) |
| 165. C22×C3 | C2×#732 | semidirect |
| 167. C2×D3 | C2×#732 | semidirect |
| 171. Dic3 | C2×#732 | semidirect |
| 203. C22 | D3×#732 | semidirect |
| 210. C3 | D4×#732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#732 | 2 |
| C2×D3×#732 | 2 |
| Dic3×#732 | 2 |
| #67×H(3,𝔽3) | 3 |
| C3×C9×#67 | 3 |
| D4×#732 | 3 |