Finite Group DatabasebetaFinite Group Databasebeta← SL(2,𝔽3)×AΣL(1,𝔽27) #14517207
Order 1944.
398 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 398 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. C33×SL(2,𝔽3) | C3 | semidirect |
| 2. SL(2,𝔽3)×3−1+2 | C3 | semidirect |
| 3. SL(2,𝔽3)×H(3,𝔽3) | C3 | semidirect |
| 4. Q8×AΣL(1,𝔽27) | C3 | semidirect |
| 5. #10619585 | C3 | semidirect |
| 6. #10619583 | C3 | semidirect |
| 7. #10619580 | C3 | semidirect |
| 11. C33×Q8 | C32 | semidirect |
| 17. C32×SL(2,𝔽3) | C32 | semidirect |
| 18. Q8×3−1+2 | C32 | semidirect |
| 19. Q8×H(3,𝔽3) | C32 | semidirect |
| 21. Q8⋊H(3,𝔽3) | C32 | semidirect |
| 22. #6204 | C32 | semidirect |
| 41. AΣL(1,𝔽27) | SL(2,𝔽3) | direct (N × H) |
| 82. C33 | C3×SL(2,𝔽3) | semidirect |
| 85. 3−1+2 | C3×SL(2,𝔽3) | semidirect |
| 88. H(3,𝔽3) | C3×SL(2,𝔽3) | semidirect |
| 97. SL(2,𝔽3) | AΣL(1,𝔽27) | direct (N × H) |
| 132. Q8 | C3×AΣL(1,𝔽27) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×SL(2,𝔽3) | 3 |
| SL(2,𝔽3)×3−1+2 | 3 |
| SL(2,𝔽3)×H(3,𝔽3) | 3 |
| Q8×AΣL(1,𝔽27) | 3 |
| #10619585 | 3 |
| #10619583 | 3 |
| #10619580 | 3 |
| C2×C3×AΣL(1,𝔽27) | 4 |