Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
428 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 76 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. #22582470 | C3 | semidirect |
| 4. #22582469 | C3 | semidirect |
| 5. C37×#6867 | C3 | semidirect |
| 24. C3×C9×C37 | 3−1+2 | semidirect |
| 29. C3×#66524 | 3−1+2 | semidirect |
| 50. #6867 | C37⋊C3 | semidirect |
| 66. C37 | #10624767 | semidirect |
| 82. C3×C9 | #11758606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C9×C37⋊C3 | 3 |
| #22582552 | 3 |
| #22582470 | 3 |
| #22582469 | 3 |
| C37×#6867 | 3 |
| #10624767 | 37 |