Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
758 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 310 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. #22582602 | C3 | semidirect |
| 3. #22582596 | C3 | semidirect |
| 4. #22582581 | C3 | semidirect |
| 5. #22582571 | C3 | semidirect |
| 7. C9×#11758605 | C3 | semidirect |
| 8. #22582538 | C3 | semidirect |
| 9. C3×C92×C37 | C3 | semidirect |
| 33. C3×C9×C37 | 3−1+2 | semidirect |
| 57. C9×C37 | #737 | semidirect |
| 68. C3×C92 | C37⋊C3 | semidirect |
| 93. C37 | #10624879 | semidirect |
| 105. C3×C9 | #11758605 | semidirect |
| 122. C9 | #15688531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688531 | 3 |
| #22582602 | 3 |
| #22582596 | 3 |
| #22582581 | 3 |
| #22582571 | 3 |
| #22582558 | 3 |
| C9×#11758605 | 3 |
| #22582538 | 3 |
| C3×C92×C37 | 3 |
| #10624879 | 37 |