Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
5804 conjugacy classes of subgroups; only the 2920 normal subgroups are shown.
This group has 5804 conjugacy classes of subgroups — too many to draw. Only its 2920 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×#15688532 | C3 | direct (N × H) |
| 2. C32×#11758608 | C3 | semidirect |
| 3. C32×#11758605 | C3 | semidirect |
| 4. C32×#11758606 | C3 | semidirect |
| 6. C33×#66524 | C3 | semidirect |
| 7. C32×C9×C37⋊C3 | C3 | semidirect |
| 8. C32×3−1+2×C37 | C3 | semidirect |
| 10. #15688532 | C32 | direct (N × H) |
| 11. C3×#11758608 | C32 | semidirect |
| 12. C3×#11758605 | C32 | semidirect |
| 13. C3×#11758606 | C32 | semidirect |
| 19. C32×#66524 | C32 | semidirect |
| 20. C3×C9×C37⋊C3 | C32 | semidirect |
| 22. C3×3−1+2×C37 | C32 | semidirect |
| 29. 3−1+2×C37 | C33 | semidirect |
| 32. #11758608 | C33 | semidirect |
| 37. C3×#66524 | C33 | semidirect |
| 38. #11758606 | C33 | semidirect |
| 39. #11758605 | C33 | semidirect |
| 40. C9×C37⋊C3 | C33 | semidirect |
| 43. C32×C37 | #737 | semidirect |
| 57. C32×3−1+2 | C37⋊C3 | semidirect |
| 62. C3×C37 | C3×#737 | semidirect |
| 71. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 80. C37 | C32×#737 | semidirect |
| 89. 3−1+2 | C32×C37⋊C3 | semidirect |
| 101. C32 | #15688532 | direct (N × H) |
| 111. C3 | C3×#15688532 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688532 | 3 |
| C32×#11758608 | 3 |
| C32×#11758605 | 3 |
| C32×#11758606 | 3 |
| C32×C32⋊(C37⋊C3) | 3 |
| C33×#66524 | 3 |
| C32×C9×C37⋊C3 | 3 |
| C32×3−1+2×C37 | 3 |
| C32×#737 | 37 |