Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1484 conjugacy classes of subgroups; only the 652 normal subgroups are shown.
This group has 1484 conjugacy classes of subgroups — too many to draw. Only its 652 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 |
|---|---|---|
| 3. C3×#15688506 | C3 | semidirect |
| 4. C3×#15688505 | C3 | semidirect |
| 5. C3×#15688504 | C3 | semidirect |
| 6. C9⋊C9×C37⋊C3 | C3 | direct (N × H) |
| 7. C3×C37×C9⋊C9 | C3 | semidirect |
| 13. C3×C9×C37⋊C3 | C9 | semidirect |
| 16. #15688506 | C32 | semidirect |
| 17. #15688505 | C32 | semidirect |
| 18. #15688504 | C32 | semidirect |
| 21. C37×C9⋊C9 | C32 | semidirect |
| 27. C3×C9×C37 | C3×C9 | semidirect |
| 32. C3×#66524 | C3×C9 | semidirect |
| 37. C9×C37⋊C3 | C3×C9 | semidirect |
| 42. C3×C37⋊C3 | C9⋊C9 | direct (N × H) |
| 46. C9×C37 | C32×C9 | semidirect |
| 49. #66524 | C32×C9 | semidirect |
| 56. C3×C9⋊C9 | C37⋊C3 | direct (N × H) |
| 57. C3×C37 | C3×C9⋊C9 | semidirect |
| 60. C37⋊C3 | C3×C9⋊C9 | direct (N × H) |
| 74. C9⋊C9 | C3×C37⋊C3 | direct (N × H) |
| 75. C37 | C32×C9⋊C9 | semidirect |
| 89. C3×C9 | C9×C37⋊C3 | semidirect |
| 102. C9 | C3×C9×C37⋊C3 | semidirect |
| 104. C3 | C9⋊C9×C37⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C37⋊C3 | 3 |
| C3×#15688506 | 3 |
| C3×#15688505 | 3 |
| C3×#15688504 | 3 |
| C9⋊C9×C37⋊C3 | 3 |
| C3×C37×C9⋊C9 | 3 |
| C32×C9⋊C9 | 37 |