Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1688 conjugacy classes of subgroups; only the 493 normal subgroups are shown.
This group has 1688 conjugacy classes of subgroups — too many to draw. Only its 493 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 |
|---|---|---|
| 2. C32×C9×C37⋊C3 | C3 | semidirect |
| 3. H(3,𝔽3)×#66524 | C3 | semidirect |
| 4. C9×C32⋊(C37⋊C3) | C3 | semidirect |
| 5. #22582539 | C3 | semidirect |
| 6. C32⋊C9×C37⋊C3 | C3 | semidirect |
| 7. C9×H(3,𝔽3)×C37 | C3 | semidirect |
| 10. H(3,𝔽3)×C37⋊C3 | C9 | direct (N × H) |
| 11. C32×#66524 | C32 | semidirect |
| 15. C3×C9×C37⋊C3 | C32 | semidirect |
| 16. C3×C9×C37⋊C3 | C32 | semidirect |
| 17. C32⋊#66524 | C32 | semidirect |
| 18. #15688502 | C32 | semidirect |
| 20. C32×C9×C37 | C32 | semidirect |
| 21. C37×C32⋊C9 | C32 | semidirect |
| 25. C32×C37⋊C3 | C3×C9 | semidirect |
| 28. H(3,𝔽3)×C37 | C3×C9 | semidirect |
| 32. C32⋊(C37⋊C3) | C3×C9 | semidirect |
| 39. C9×C37⋊C3 | H(3,𝔽3) | direct (N × H) |
| 43. C32×C37 | C32×C9 | semidirect |
| 49. C3×C37⋊C3 | C32×C9 | semidirect |
| 53. C9×C37 | C3×H(3,𝔽3) | semidirect |
| 55. #66524 | C3×H(3,𝔽3) | semidirect |
| 61. C9×H(3,𝔽3) | C37⋊C3 | direct (N × H) |
| 68. C37⋊C3 | C9×H(3,𝔽3) | direct (N × H) |
| 79. C32×C9 | C3×C37⋊C3 | semidirect |
| 82. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 83. C37 | C3×C9×H(3,𝔽3) | semidirect |
| 91. H(3,𝔽3) | C9×C37⋊C3 | direct (N × H) |
| 111. C32 | C3×C9×C37⋊C3 | semidirect |
| 116. C9 | H(3,𝔽3)×C37⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| C32×C9×C37⋊C3 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| C9×C32⋊(C37⋊C3) | 3 |
| #22582539 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| C3×C9×H(3,𝔽3) | 37 |