Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
902 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 902 conjugacy classes of subgroups — too many to draw. Only its 298 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 |
|---|---|---|
| 2. C3×Q8×3−1+2 | C3 | semidirect |
| 3. C3×#6204 | C3 | semidirect |
| 4. SL(2,𝔽3)×3−1+2 | C3 | direct (N × H) |
| 5. C3×C9⋊SL(2,𝔽3) | C3 | semidirect |
| 6. C3×C9×SL(2,𝔽3) | C3 | semidirect |
| 15. Q8×3−1+2 | C32 | semidirect |
| 16. C3×Q8×C9 | C32 | semidirect |
| 17. #6204 | C32 | semidirect |
| 18. C3×Q8⋊C9 | C32 | semidirect |
| 19. C9⋊SL(2,𝔽3) | C32 | semidirect |
| 20. C9×SL(2,𝔽3) | C32 | semidirect |
| 34. C3×3−1+2 | SL(2,𝔽3) | direct (N × H) |
| 41. C3×SL(2,𝔽3) | 3−1+2 | direct (N × H) |
| 44. Q8×C9 | C33 | semidirect |
| 45. Q8⋊C9 | C33 | semidirect |
| 68. 3−1+2 | C3×SL(2,𝔽3) | direct (N × H) |
| 71. C3×C9 | C3×SL(2,𝔽3) | semidirect |
| 73. C3×Q8 | C3×3−1+2 | semidirect |
| 76. SL(2,𝔽3) | C3×3−1+2 | direct (N × H) |
| 99. C9 | C32×SL(2,𝔽3) | semidirect |
| 100. Q8 | C32×3−1+2 | semidirect |
| 110. C3 | SL(2,𝔽3)×3−1+2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×SL(2,𝔽3) | 3 |
| C3×Q8×3−1+2 | 3 |
| C3×#6204 | 3 |
| SL(2,𝔽3)×3−1+2 | 3 |
| C3×C9⋊SL(2,𝔽3) | 3 |
| C3×C9×SL(2,𝔽3) | 3 |
| C2×C32×3−1+2 | 4 |