Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
5490 conjugacy classes of subgroups; only the 2878 normal subgroups are shown.
This group has 5490 conjugacy classes of subgroups — too many to draw. Only its 2878 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C34×C37⋊C3 |
| commutator, socle, cosocle | C3×C37 | C35 |
| Fitting | C37×3−1+4 | C3 |
| prime radical | C37⋊H(5,𝔽3) | C3 |
| hypercenter | 3−1+4 | C37⋊C3 |
| hypocenter | C37 | #10624943 |
| LCS | G ▷ C3×C37 ▷ C37 | |
| UCS | C1 ◁ C3 ◁ 3−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22582680 | C3 | semidirect |
| 2. #22582679 | C3 | semidirect |
| 3. #22582678 | C3 | semidirect |
| 4. #22582677 | C3 | semidirect |
| 6. C3×#15688532 | C3 | semidirect |
| 7. C3×#15688530 | C3 | semidirect |
| 8. #737×C37⋊C3 | C3 | semidirect |
| 9. C37×3−1+4 | C3 | semidirect |
| 10. #15688532 | C32 | semidirect |
| 11. #15688532 | C32 | semidirect |
| 12. #15688532 | C32 | semidirect |
| 13. #15688532 | C32 | semidirect |
| 14. #15688532 | C32 | semidirect |
| 15. #15688532 | C32 | semidirect |
| 16. #15688531 | C32 | semidirect |
| 17. #15688530 | C32 | semidirect |
| 18. #15688530 | C32 | semidirect |
| 19. #15688530 | C32 | semidirect |
| 20. #15688530 | C32 | semidirect |
| 21. C3×#11758608 | C32 | semidirect |
| 22. C3×#11758608 | C32 | semidirect |
| 23. C3×#11758605 | C32 | semidirect |
| 24. C3×#11758606 | C32 | semidirect |
| 25. 3−1+2×C37⋊C3 | C32 | semidirect |
| 28. C32×#66524 | C32 | semidirect |
| 29. C3×C9×C37⋊C3 | C32 | semidirect |
| 30. C37×#737 | C32 | semidirect |
| 31. C3×3−1+2×C37 | C32 | semidirect |
| 72. 3−1+4 | C37⋊C3 | semidirect |
| 92. #737 | C3×C37⋊C3 | semidirect |
| 98. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 104. C37 | #10624943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582680 | 3 |
| #22582679 | 3 |
| #22582678 | 3 |
| #22582677 | 3 |
| C37⋊H(5,𝔽3) | 3 |
| C3×#15688532 | 3 |
| C3×#15688530 | 3 |
| #737×C37⋊C3 | 3 |
| C37×3−1+4 | 3 |
| #10624943 | 37 |