Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
400 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 88 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. A4×#732 | C2 | direct (N × H) |
| 2. C2×A4×H(3,𝔽3) | C3 | semidirect |
| 3. C2×C3×C9×A4 | C3 | semidirect |
| 4. C23×#732 | C3 | semidirect |
| 5. C2×#66362 | C3 | semidirect |
| 6. C2×#66358 | C3 | semidirect |
| 8. A4×H(3,𝔽3) | C2×C3 | semidirect |
| 9. C3×C9×A4 | C2×C3 | semidirect |
| 12. C22×#732 | C2×C3 | semidirect |
| 13. #66362 | C2×C3 | semidirect |
| 14. #66358 | C2×C3 | semidirect |
| 18. C23×H(3,𝔽3) | C32 | semidirect |
| 19. C23×C3×C9 | C32 | semidirect |
| 21. C2×C22⋊H(3,𝔽3) | C32 | semidirect |
| 22. C2×C3×C22⋊C9 | C32 | semidirect |
| 31. C2×#732 | A4 | direct (N × H) |
| 36. C22×H(3,𝔽3) | C2×C32 | semidirect |
| 39. C22×C3×C9 | C2×C32 | semidirect |
| 41. C22⋊H(3,𝔽3) | C2×C32 | semidirect |
| 42. C3×C22⋊C9 | C2×C32 | semidirect |
| 49. #732 | C2×A4 | direct (N × H) |
| 65. C2×H(3,𝔽3) | C3×A4 | semidirect |
| 71. C2×C3×C9 | C3×A4 | semidirect |
| 91. H(3,𝔽3) | C2×C3×A4 | semidirect |
| 95. C3×C9 | C2×C3×A4 | semidirect |
| 101. C2×A4 | #732 | direct (N × H) |
| 128. A4 | C2×#732 | direct (N × H) |
| 138. C23 | C3×#732 | semidirect |
| 153. C22 | C2×C3×#732 | semidirect |
| 162. C2 | A4×#732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×#732 | 2 |
| C2×A4×H(3,𝔽3) | 3 |
| C2×C3×C9×A4 | 3 |
| C23×#732 | 3 |
| C2×#66362 | 3 |
| C2×#66358 | 3 |
| C2×C3×#732 | 4 |