Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
230 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 52 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. SL(2,𝔽3)×3−1+2 | C3 | semidirect |
| 3. C3×C9×SL(2,𝔽3) | C3 | semidirect |
| 4. Q8×#731 | C3 | semidirect |
| 5. #10619582 | C3 | semidirect |
| 6. #10619578 | C3 | semidirect |
| 7. #10619574 | C3 | semidirect |
| 13. Q8×3−1+2 | C32 | semidirect |
| 15. C3×Q8×C9 | C32 | semidirect |
| 18. #6204 | C32 | semidirect |
| 19. C3×Q8⋊C9 | C32 | semidirect |
| 40. #731 | SL(2,𝔽3) | direct (N × H) |
| 73. 3−1+2 | C3×SL(2,𝔽3) | semidirect |
| 81. C3×C9 | C3×SL(2,𝔽3) | semidirect |
| 87. SL(2,𝔽3) | #731 | direct (N × H) |
| 113. Q8 | C3×#731 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| SL(2,𝔽3)×3−1+2 | 3 |
| SL(2,𝔽3)×H(3,𝔽3) | 3 |
| C3×C9×SL(2,𝔽3) | 3 |
| Q8×#731 | 3 |
| #10619582 | 3 |
| #10619578 | 3 |
| #10619574 | 3 |
| C2×C3×#731 | 4 |