Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
884 conjugacy classes of subgroups; only the 364 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 364 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 |
|---|---|---|
| 3. #22582581 | C3 | direct (N × H) |
| 4. C3×#15688506 | C3 | semidirect |
| 5. C3×#15688505 | C3 | semidirect |
| 6. C3×#15688504 | C3 | semidirect |
| 8. C3×C92×C37 | C3 | semidirect |
| 17. #15688506 | C32 | semidirect |
| 18. #15688505 | C32 | semidirect |
| 19. #15688504 | C32 | semidirect |
| 24. C92×C37 | C32 | semidirect |
| 31. C3×C9×C37 | 3−1+2 | semidirect |
| 32. C3×C9×C37 | 3−1+2 | semidirect |
| 54. C9×C37 | C3×3−1+2 | semidirect |
| 55. C9×C37 | C3×3−1+2 | semidirect |
| 66. C3×C92 | C37⋊C3 | semidirect |
| 67. C3×C37 | #6896 | semidirect |
| 87. C92 | C3×C37⋊C3 | semidirect |
| 88. C37 | C3×#6896 | semidirect |
| 103. C3×C9 | #11758605 | semidirect |
| 104. C3×C9 | #11758606 | semidirect |
| 120. C9 | C3×#11758606 | semidirect |
| 121. C9 | C3×#11758605 | semidirect |
| 123. C3 | #22582581 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758605 | 3 |
| C32×#11758606 | 3 |
| #22582581 | 3 |
| C3×#15688506 | 3 |
| C3×#15688505 | 3 |
| C3×#15688504 | 3 |
| C3×#15688502 | 3 |
| C3×C92×C37 | 3 |
| C3×#6896 | 37 |