Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
384 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11757809 | 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 |
| 30. C2×#732 | A4 | semidirect |
| 35. C22×H(3,𝔽3) | C2×C32 | semidirect |
| 38. C22×C3×C9 | C2×C32 | semidirect |
| 40. C22⋊H(3,𝔽3) | C2×C32 | semidirect |
| 41. C3×C22⋊C9 | C2×C32 | semidirect |
| 47. #732 | C2×A4 | semidirect |
| 63. C2×H(3,𝔽3) | C3×A4 | semidirect |
| 67. C2×C3×C9 | C3×A4 | semidirect |
| 87. H(3,𝔽3) | C2×C3×A4 | semidirect |
| 89. C3×C9 | C2×C3×A4 | semidirect |
| 128. C23 | #6911 | semidirect |
| 142. C22 | C2×#6911 | semidirect |
| 150. C2 | #11757809 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757809 | 2 |
| C2×A4×H(3,𝔽3) | 3 |
| C2×C3×C9⋊A4 | 3 |
| C23×#732 | 3 |
| C2×#66362 | 3 |
| C2×#66358 | 3 |
| C2×#6911 | 4 |