Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
1384 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1384 conjugacy classes of subgroups — too many to draw. Only its 271 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. C3×A4×3−1+2 | C3 | semidirect |
| 2. C3×A4×H(3,𝔽3) | C3 | semidirect |
| 3. C22×#6911 | C3 | semidirect |
| 4. #11757852 | C3 | semidirect |
| 5. #11757837 | C3 | semidirect |
| 6. #11757809 | C3 | semidirect |
| 7. A4×#732 | C3 | semidirect |
| 12. C22×C3×3−1+2 | C32 | semidirect |
| 13. C22×C3×H(3,𝔽3) | C32 | semidirect |
| 15. C3×C22⋊H(3,𝔽3) | C32 | semidirect |
| 16. C3×#1094 | C32 | semidirect |
| 21. A4×H(3,𝔽3) | C32 | semidirect |
| 22. A4×H(3,𝔽3) | C32 | semidirect |
| 23. C3×C9⋊A4 | C32 | semidirect |
| 24. C3×C9×A4 | C32 | semidirect |
| 25. C22×#732 | C32 | semidirect |
| 26. #66362 | C32 | semidirect |
| 27. #66358 | C32 | semidirect |
| 33. #6911 | A4 | direct (N × H) |
| 51. C22×H(3,𝔽3) | C33 | semidirect |
| 52. C22×C3×C9 | C33 | semidirect |
| 56. C22⋊H(3,𝔽3) | C33 | semidirect |
| 58. C3×C22⋊C9 | C33 | semidirect |
| 68. C3×3−1+2 | C3×A4 | semidirect |
| 75. C3×H(3,𝔽3) | C3×A4 | semidirect |
| 79. #732 | C3×A4 | semidirect |
| 123. H(3,𝔽3) | C32×A4 | semidirect |
| 127. C3×C9 | C32×A4 | semidirect |
| 141. A4 | #6911 | direct (N × H) |
| 164. C22 | C3×#6911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×A4×3−1+2 | 3 |
| C3×A4×H(3,𝔽3) | 3 |
| C22×#6911 | 3 |
| #11757852 | 3 |
| #11757837 | 3 |
| #11757809 | 3 |
| A4×#732 | 3 |
| C3×#6911 | 4 |