Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
758 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 280 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×Q8×3−1+2 | C3 | semidirect |
| 3. C3×#6204 | C3 | semidirect |
| 4. C32×Q8⋊C9 | C3 | semidirect |
| 5. #10619916 | C3 | direct (N × H) |
| 6. C3×C9⋊SL(2,𝔽3) | C3 | semidirect |
| 7. C3×C9×SL(2,𝔽3) | C3 | semidirect |
| 13. Q8×3−1+2 | C32 | semidirect |
| 16. #6204 | C32 | semidirect |
| 20. C3×Q8⋊C9 | C32 | semidirect |
| 21. C9⋊SL(2,𝔽3) | C32 | semidirect |
| 22. C9×SL(2,𝔽3) | C32 | semidirect |
| 36. C3×3−1+2 | SL(2,𝔽3) | semidirect |
| 69. 3−1+2 | C3×SL(2,𝔽3) | semidirect |
| 78. C3×Q8 | #737 | semidirect |
| 102. Q8 | C3×#737 | semidirect |
| 110. C3 | #10619916 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×3−1+2 | 3 |
| C3×Q8⋊H(3,𝔽3) | 3 |
| C3×#6204 | 3 |
| C32×Q8⋊C9 | 3 |
| #10619916 | 3 |
| C3×C9⋊SL(2,𝔽3) | 3 |
| C3×C9×SL(2,𝔽3) | 3 |
| C2×C3×#737 | 4 |