Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
376 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11757801 | C2 | direct (N × H) |
| 2. C2×C3×C22⋊H(3,𝔽3) | C3 | semidirect |
| 3. C2×A4×3−1+2 | C3 | semidirect |
| 4. C2×A4×H(3,𝔽3) | C3 | semidirect |
| 5. C23×AΣL(1,𝔽27) | C3 | semidirect |
| 6. C2×#66368 | C3 | semidirect |
| 7. C2×#66366 | C3 | semidirect |
| 8. C2×#66363 | C3 | semidirect |
| 10. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 11. A4×3−1+2 | C2×C3 | semidirect |
| 12. A4×H(3,𝔽3) | C2×C3 | semidirect |
| 15. C22×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 16. #66368 | C2×C3 | semidirect |
| 17. #66366 | C2×C3 | semidirect |
| 18. #66363 | C2×C3 | semidirect |
| 20. C23×C33 | C32 | semidirect |
| 23. C2×C32×A4 | C32 | semidirect |
| 24. C23×3−1+2 | C32 | semidirect |
| 30. C2×#1094 | C32 | semidirect |
| 42. C2×AΣL(1,𝔽27) | A4 | semidirect |
| 45. C22×C33 | C2×C32 | semidirect |
| 48. C32×A4 | C2×C32 | semidirect |
| 51. C22×3−1+2 | C2×C32 | semidirect |
| 59. #1094 | C2×C32 | semidirect |
| 69. AΣL(1,𝔽27) | C2×A4 | semidirect |
| 88. C2×C33 | C3×A4 | semidirect |
| 94. C2×3−1+2 | C3×A4 | semidirect |
| 129. C33 | C2×C3×A4 | semidirect |
| 133. 3−1+2 | C2×C3×A4 | semidirect |
| 200. C23 | #6909 | semidirect |
| 219. C22 | C2×#6909 | semidirect |
| 230. C2 | #11757801 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757801 | 2 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×A4×3−1+2 | 3 |
| C2×A4×H(3,𝔽3) | 3 |
| C23×AΣL(1,𝔽27) | 3 |
| C2×#66368 | 3 |
| C2×#66366 | 3 |
| C2×#66363 | 3 |
| C2×#6909 | 4 |