Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
228 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22582571 | C3 | semidirect |
| 4. C3×#15688504 | C3 | semidirect |
| 5. 3−1+2⋊#66524 | C3 | semidirect |
| 6. 3−1+2⋊#66524 | C3 | semidirect |
| 7. #22582478 | C3 | semidirect |
| 8. #22582478 | C3 | semidirect |
| 11. #22582469 | C3 | semidirect |
| 12. #22582469 | C3 | semidirect |
| 13. C37×#6894 | C3 | semidirect |
| 66. C3×#66524 | 3−1+2 | semidirect |
| 95. #6894 | C37⋊C3 | semidirect |
| 139. C37 | #10624789 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688517 | 3 |
| #22582571 | 3 |
| #22582559 | 3 |
| C3×#15688504 | 3 |
| 3−1+2⋊#66524 | 3 |
| #22582478 | 3 |
| #22582475 | 3 |
| #22582469 | 3 |
| C37×#6894 | 3 |
| #10624789 | 37 |