Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
167 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 167 conjugacy classes of subgroups — too many to draw. Only its 55 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. Q8×C9⋊C9 | C3 | semidirect |
| 6. C9⋊(Q8⋊C9) | C3 | semidirect |
| 7. C9⋊(Q8⋊C9) | C3 | semidirect |
| 8. (Q8⋊C9)⋊C9 | C3 | semidirect |
| 9. (Q8⋊C9)⋊C9 | C3 | semidirect |
| 10. (Q8⋊C9)⋊C9 | C3 | semidirect |
| 11. (Q8⋊C9)⋊C9 | C3 | semidirect |
| 12. (Q8⋊C9)⋊C9 | C3 | semidirect |
| 13. C9×Q8⋊C9 | C3 | semidirect |
| 54. C9⋊C9 | SL(2,𝔽3) | semidirect |
| 151. Q8 | #6897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9⋊C9 | 3 |
| (C3×SL(2,𝔽3))⋊C9 | 3 |
| C9⋊(Q8⋊C9) | 3 |
| (Q8⋊C9)⋊C9 | 3 |
| C9×Q8⋊C9 | 3 |
| C2×#6897 | 4 |