Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1062 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 1062 conjugacy classes of subgroups — too many to draw. Only its 268 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. C37⋊H(5,𝔽3) | C3 | semidirect |
| 2. C3×#15688532 | C3 | semidirect |
| 3. #22582648 | C3 | semidirect |
| 4. #22582647 | C3 | semidirect |
| 5. #22582646 | C3 | semidirect |
| 6. #22582645 | C3 | semidirect |
| 7. C3×#15688518 | C3 | semidirect |
| 8. #732×C37⋊C3 | C3 | semidirect |
| 9. C37×#6911 | C3 | semidirect |
| 11. C3×#11758608 | C32 | semidirect |
| 12. C3×#11758605 | C32 | semidirect |
| 13. C3×#11758606 | C32 | semidirect |
| 16. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 18. H(3,𝔽3)×C37⋊C3 | C32 | semidirect |
| 19. C32×#66524 | C32 | semidirect |
| 20. C3×C9×C37⋊C3 | C32 | semidirect |
| 21. #15688519 | C32 | semidirect |
| 22. #15688518 | C32 | semidirect |
| 23. #15688518 | C32 | semidirect |
| 24. #15688518 | C32 | semidirect |
| 25. #15688518 | C32 | semidirect |
| 26. C3×3−1+2×C37 | C32 | semidirect |
| 27. C3×H(3,𝔽3)×C37 | C32 | semidirect |
| 28. C37×#732 | C32 | semidirect |
| 74. #6911 | C37⋊C3 | semidirect |
| 87. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 93. C3×H(3,𝔽3) | C3×C37⋊C3 | semidirect |
| 101. #732 | C3×C37⋊C3 | semidirect |
| 102. C37 | #10624932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37⋊H(5,𝔽3) | 3 |
| C3×#15688532 | 3 |
| #22582648 | 3 |
| #22582647 | 3 |
| #22582646 | 3 |
| #22582645 | 3 |
| C3×#15688518 | 3 |
| #732×C37⋊C3 | 3 |
| C37×#6911 | 3 |
| #10624932 | 37 |