Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
698 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 292 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. #22582605 | C3 | semidirect |
| 3. #22582599 | C3 | semidirect |
| 4. #22582583 | C3 | semidirect |
| 5. #22582571 | C3 | semidirect |
| 6. #22582567 | C3 | semidirect |
| 8. #22582538 | C3 | semidirect |
| 9. #22582538 | C3 | semidirect |
| 10. C3×C37×C9⋊C9 | C3 | semidirect |
| 39. C3×C9×C37 | 3−1+2 | semidirect |
| 77. C3×C9⋊C9 | C37⋊C3 | semidirect |
| 107. C37 | #10624887 | semidirect |
| 120. C3×C9 | #11758605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688531 | 3 |
| #22582605 | 3 |
| #22582599 | 3 |
| #22582583 | 3 |
| #22582571 | 3 |
| #22582567 | 3 |
| #22582558 | 3 |
| #22582538 | 3 |
| C3×C37×C9⋊C9 | 3 |
| #10624887 | 37 |