Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 1. #22582576 | C3 | semidirect |
| 2. #22582575 | C3 | semidirect |
| 3. #22582535 | C3 | semidirect |
| 5. #22582471 | C3 | semidirect |
| 6. #22582471 | C3 | semidirect |
| 7. #22582471 | C3 | semidirect |
| 8. #22582470 | C3 | semidirect |
| 9. #22582470 | C3 | semidirect |
| 13. C37×#6867 | C3 | semidirect |
| 102. #6867 | C37⋊C3 | semidirect |
| 138. C37 | #10624810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582576 | 3 |
| #22582575 | 3 |
| #22582535 | 3 |
| C3×#15688502 | 3 |
| #22582471 | 3 |
| #22582470 | 3 |
| #22582467 | 3 |
| C37×#6867 | 3 |
| #10624810 | 37 |