Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
936 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 268 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. #22582652 | C3 | semidirect |
| 4. #22582651 | C3 | semidirect |
| 5. #22582650 | C3 | semidirect |
| 6. #22582649 | C3 | semidirect |
| 7. C3×#15688520 | C3 | semidirect |
| 8. #733×C37⋊C3 | C3 | semidirect |
| 9. C37×#6912 | C3 | semidirect |
| 72. #6912 | C37⋊C3 | semidirect |
| 98. C37 | #10624933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582679 | 3 |
| C3×#15688532 | 3 |
| #22582652 | 3 |
| #22582651 | 3 |
| #22582650 | 3 |
| #22582649 | 3 |
| C3×#15688520 | 3 |
| #733×C37⋊C3 | 3 |
| C37×#6912 | 3 |
| #10624933 | 37 |