Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
848 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 451 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. #22582614 | C3 | semidirect |
| 3. #22582613 | C3 | semidirect |
| 4. #22582612 | C3 | semidirect |
| 5. C27⋊C3×C37⋊C3 | C3 | semidirect |
| 6. C3×C27×C37⋊C3 | C3 | semidirect |
| 7. C37×#6903 | C3 | semidirect |
| 14. #15688511 | C32 | semidirect |
| 15. #15688510 | C32 | semidirect |
| 16. #15688509 | C32 | semidirect |
| 17. C3×#11758601 | C32 | semidirect |
| 20. C27×C37⋊C3 | C32 | semidirect |
| 21. C27×C37⋊C3 | C32 | semidirect |
| 23. C37×C27⋊C3 | C32 | semidirect |
| 24. C3×C27×C37 | C32 | semidirect |
| 55. #6903 | C37⋊C3 | direct (N × H) |
| 61. C37⋊C3 | #6903 | direct (N × H) |
| 72. C27⋊C3 | C3×C37⋊C3 | semidirect |
| 78. C3×C27 | C3×C37⋊C3 | semidirect |
| 79. C37 | C3×#6903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #737×C37⋊C3 | 3 |
| #22582614 | 3 |
| #22582613 | 3 |
| #22582612 | 3 |
| C27⋊C3×C37⋊C3 | 3 |
| C3×C27×C37⋊C3 | 3 |
| C37×#6903 | 3 |
| C3×#6903 | 37 |