Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
848 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 432 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. #22582732 | C3 | direct (N × H) |
| 2. C3×#15688543 | C3 | semidirect |
| 3. C3×#15688542 | C3 | semidirect |
| 4. C3×#15688541 | C3 | semidirect |
| 5. C3×(C37⋊C3)⋊C27 | C3 | semidirect |
| 6. C32×#11758603 | C3 | semidirect |
| 8. #15688543 | C32 | semidirect |
| 9. #15688542 | C32 | semidirect |
| 10. #15688541 | C32 | semidirect |
| 11. (C37⋊C3)⋊C27 | C32 | semidirect |
| 16. C3×#11758603 | C32 | semidirect |
| 66. C3×C37 | #6903 | semidirect |
| 87. C37 | C3×#6903 | semidirect |
| 121. C3 | #22582732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582732 | 3 |
| C3×#15688543 | 3 |
| C3×#15688542 | 3 |
| C3×#15688541 | 3 |
| C3×(C37⋊C3)⋊C27 | 3 |
| C32×#11758603 | 3 |
| C3×#15688532 | 3 |
| C3×#6903 | 37 |