Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
268 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 268 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)×H(3,𝔽3) | C3 | semidirect |
| 2. C3×C9×SL(2,𝔽3) | C3 | semidirect |
| 3. Q8×#732 | C3 | semidirect |
| 4. #10619579 | C3 | semidirect |
| 5. #10619575 | C3 | semidirect |
| 11. Q8×H(3,𝔽3) | C32 | semidirect |
| 12. C3×Q8×C9 | C32 | semidirect |
| 14. Q8⋊H(3,𝔽3) | C32 | semidirect |
| 15. C3×Q8⋊C9 | C32 | semidirect |
| 29. #732 | SL(2,𝔽3) | direct (N × H) |
| 55. H(3,𝔽3) | C3×SL(2,𝔽3) | semidirect |
| 59. C3×C9 | C3×SL(2,𝔽3) | semidirect |
| 65. SL(2,𝔽3) | #732 | direct (N × H) |
| 87. Q8 | C3×#732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| SL(2,𝔽3)×H(3,𝔽3) | 3 |
| C3×C9×SL(2,𝔽3) | 3 |
| Q8×#732 | 3 |
| #10619579 | 3 |
| #10619575 | 3 |
| C2×C3×#732 | 4 |