Finite Group DatabasebetaFinite Group DatabasebetaOrder 972.
186 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 44 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×C3×3−1+2 | C3 | semidirect |
| 2. C3×C22⋊H(3,𝔽3) | C3 | semidirect |
| 3. C3×C22⋊H(3,𝔽3) | C3 | semidirect |
| 4. C3×#1094 | C3 | semidirect |
| 5. #66366 | C3 | semidirect |
| 10. C32×A4 | C32 | semidirect |
| 13. C22×3−1+2 | C32 | semidirect |
| 23. #1094 | C32 | semidirect |
| 26. C3×3−1+2 | A4 | semidirect |
| 54. 3−1+2 | C3×A4 | semidirect |
| 92. C22 | #6909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×3−1+2 | 3 |
| C3×C22⋊H(3,𝔽3) | 3 |
| C3×#1094 | 3 |
| #66366 | 3 |
| #6909 | 4 |