Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
960 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 286 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. C3×#15688531 | C3 | semidirect |
| 2. #22582661 | C3 | semidirect |
| 3. #22582652 | C3 | semidirect |
| 4. #22582648 | C3 | semidirect |
| 5. #22582643 | C3 | semidirect |
| 6. #22582638 | C3 | semidirect |
| 7. #22582633 | C3 | semidirect |
| 8. C3×C37×#737 | C3 | semidirect |
| 12. #15688531 | C32 | semidirect |
| 13. #15688531 | C32 | semidirect |
| 19. #15688521 | C32 | semidirect |
| 21. #15688516 | C32 | semidirect |
| 22. #15688513 | C32 | semidirect |
| 28. C3×3−1+2×C37 | C32 | semidirect |
| 31. C32×C9×C37 | C32 | semidirect |
| 76. C3×#737 | C37⋊C3 | semidirect |
| 101. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 106. C32×C9 | C3×C37⋊C3 | semidirect |
| 111. C37 | #10624929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688531 | 3 |
| #22582661 | 3 |
| #22582652 | 3 |
| #22582648 | 3 |
| #22582643 | 3 |
| #22582638 | 3 |
| #22582633 | 3 |
| C3×C37×#737 | 3 |
| #10624929 | 37 |