Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
472 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 472 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. #11757852 | C2 | direct (N × H) |
| 2. C23×C3×3−1+2 | C3 | semidirect |
| 3. C2×C3×C22⋊H(3,𝔽3) | C3 | semidirect |
| 4. C2×#66358 | C3 | semidirect |
| 8. C22×C3×3−1+2 | C2×C3 | semidirect |
| 9. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 10. #66358 | C2×C3 | semidirect |
| 15. C23×C3×C9 | C32 | semidirect |
| 17. C2×C22⋊H(3,𝔽3) | C32 | semidirect |
| 20. C2×C3×3−1+2 | A4 | semidirect |
| 32. C22×C3×C9 | C2×C32 | semidirect |
| 34. C22⋊H(3,𝔽3) | C2×C32 | semidirect |
| 35. C3×3−1+2 | C2×A4 | semidirect |
| 55. C2×C3×C9 | C3×A4 | semidirect |
| 75. C3×C9 | C2×C3×A4 | semidirect |
| 110. C23 | #6911 | semidirect |
| 123. C22 | C2×#6911 | semidirect |
| 130. C2 | #11757852 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757852 | 2 |
| C23×C3×3−1+2 | 3 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×#66358 | 3 |
| C2×#6911 | 4 |