Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
986 conjugacy classes of subgroups; only the 463 normal subgroups are shown.
This group has 986 conjugacy classes of subgroups — too many to draw. Only its 463 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. #22582548 | C3 | semidirect |
| 3. #22582543 | C3 | semidirect |
| 4. #22582542 | C3 | semidirect |
| 6. #22582538 | C3 | semidirect |
| 7. #22582536 | C3 | semidirect |
| 8. C3×C9×#66524 | C3 | semidirect |
| 9. C92×C37⋊C3 | C3 | semidirect |
| 10. C37×#6887 | C3 | semidirect |
| 11. #15688531 | C9 | semidirect |
| 37. C3×C9×C37 | C3×C9 | semidirect |
| 43. #11758608 | C3×C9 | semidirect |
| 49. #11758606 | C3×C9 | semidirect |
| 50. #11758605 | C3×C9 | semidirect |
| 52. C9×C37⋊C3 | C3×C9 | semidirect |
| 66. #66524 | #737 | semidirect |
| 74. #6887 | C37⋊C3 | semidirect |
| 105. C37 | C9×#737 | semidirect |
| 119. C3×C9 | C9×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688531 | 3 |
| #22582548 | 3 |
| #22582543 | 3 |
| #22582542 | 3 |
| #22582539 | 3 |
| #22582538 | 3 |
| #22582536 | 3 |
| C3×C9×#66524 | 3 |
| C92×C37⋊C3 | 3 |
| C37×#6887 | 3 |
| C9×#737 | 37 |