Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
200 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 58 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. C9×#11758608 | C3 | semidirect |
| 3. #22582538 | C3 | semidirect |
| 4. C37⋊#6862 | C3 | semidirect |
| 5. #22582458 | C3 | semidirect |
| 8. #22582449 | C3 | semidirect |
| 9. #22582448 | C3 | semidirect |
| 10. #22582447 | C3 | semidirect |
| 11. #22582447 | C3 | semidirect |
| 13. C37×#6894 | C3 | semidirect |
| 84. #6894 | C37⋊C3 | semidirect |
| 128. C37 | #10624621 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582559 | 3 |
| C9×#11758608 | 3 |
| #22582538 | 3 |
| C37⋊#6862 | 3 |
| #22582458 | 3 |
| #22582453 | 3 |
| #22582452 | 3 |
| #22582449 | 3 |
| #22582448 | 3 |
| #22582447 | 3 |
| #22582444 | 3 |
| C37×#6894 | 3 |
| #10624621 | 37 |