Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
290 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 4. #22582688 | C3 | semidirect |
| 5. C9×#11758603 | C3 | semidirect |
| 7. #15688543 | C9 | semidirect |
| 8. #15688542 | C9 | semidirect |
| 9. (C37⋊C3)⋊C27 | C9 | semidirect |
| 70. C37 | #10624681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688543 | 3 |
| C3×#15688542 | 3 |
| C3×(C37⋊C3)⋊C27 | 3 |
| #22582688 | 3 |
| C9×#11758603 | 3 |
| #22582537 | 3 |
| #10624681 | 37 |