Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
332 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 332 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. #11757799 | C2 | direct (N × H) |
| 2. C2×C3×#1094 | C3 | semidirect |
| 3. C2×#66440 | C3 | semidirect |
| 4. C2×#66437 | C3 | semidirect |
| 5. C23×AΣL(1,𝔽27) | C3 | semidirect |
| 6. C2×#66368 | C3 | semidirect |
| 7. C2×#66365 | C3 | semidirect |
| 8. C2×#66364 | C3 | semidirect |
| 9. C2×#66362 | C3 | semidirect |
| 10. C2×#66361 | C3 | semidirect |
| 12. C3×#1094 | C2×C3 | semidirect |
| 13. #66440 | C2×C3 | semidirect |
| 14. #66437 | C2×C3 | semidirect |
| 17. C22×AΣL(1,𝔽27) | C2×C3 | semidirect |
| 18. #66368 | C2×C3 | semidirect |
| 19. #66365 | C2×C3 | semidirect |
| 20. #66364 | C2×C3 | semidirect |
| 21. #66362 | C2×C3 | semidirect |
| 22. #66361 | C2×C3 | semidirect |
| 50. C2×AΣL(1,𝔽27) | A4 | semidirect |
| 81. AΣL(1,𝔽27) | C2×A4 | semidirect |
| 206. C23 | #6913 | semidirect |
| 222. C22 | C2×#6913 | semidirect |
| 230. C2 | #11757799 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757799 | 2 |
| C2×C3×#1094 | 3 |
| C2×#66440 | 3 |
| C2×#66437 | 3 |
| C23×AΣL(1,𝔽27) | 3 |
| C2×#66368 | 3 |
| C2×#66365 | 3 |
| C2×#66364 | 3 |
| C2×#66362 | 3 |
| C2×#66361 | 3 |
| C2×#6913 | 4 |