Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
828 conjugacy classes of subgroups; only the 448 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 448 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. #22582612 | C3 | semidirect |
| 4. C3×#15688511 | C3 | semidirect |
| 5. C27⋊C3×C37⋊C3 | C3 | semidirect |
| 6. C3×C37×C27⋊C3 | C3 | semidirect |
| 18. #15688511 | C32 | semidirect |
| 19. #15688511 | C32 | semidirect |
| 20. #15688510 | C32 | semidirect |
| 21. #15688509 | C32 | semidirect |
| 22. C3×#11758601 | C32 | semidirect |
| 23. C27×C37⋊C3 | C32 | semidirect |
| 26. C37×C27⋊C3 | C32 | semidirect |
| 27. C3×C27×C37 | C32 | semidirect |
| 70. C3×C27⋊C3 | C37⋊C3 | semidirect |
| 93. C27⋊C3 | C3×C37⋊C3 | semidirect |
| 96. C3×C27 | C3×C37⋊C3 | semidirect |
| 97. C37 | #10624918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688531 | 3 |
| #22582614 | 3 |
| #22582612 | 3 |
| C3×#15688511 | 3 |
| C27⋊C3×C37⋊C3 | 3 |
| C3×C37×C27⋊C3 | 3 |
| #10624918 | 37 |