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×#15688531 | C3 | direct (N × H) |
| 2. C32×#11758608 | C3 | semidirect |
| 3. C32×#11758605 | C3 | semidirect |
| 4. C32×#11758606 | C3 | semidirect |
| 6. C32×C9×C37⋊C3 | C3 | semidirect |
| 7. C33×C9×C37 | C3 | semidirect |
| 9. #15688531 | C32 | direct (N × H) |
| 10. C3×#11758608 | C32 | semidirect |
| 11. C3×#11758605 | C32 | semidirect |
| 12. C3×#11758606 | C32 | semidirect |
| 15. C3×C9×C37⋊C3 | C32 | semidirect |
| 20. C32×C9×C37 | C32 | semidirect |
| 29. C3×C9×C37 | C33 | semidirect |
| 31. #11758608 | C33 | semidirect |
| 33. #11758606 | C33 | semidirect |
| 34. #11758605 | C33 | semidirect |
| 35. C9×C37⋊C3 | C33 | semidirect |
| 38. C32×C37 | #737 | semidirect |
| 53. C33×C9 | C37⋊C3 | semidirect |
| 55. C3×C37 | C3×#737 | semidirect |
| 70. C32×C9 | C3×C37⋊C3 | semidirect |
| 71. C37 | C32×#737 | semidirect |
| 86. C3×C9 | C32×C37⋊C3 | semidirect |
| 90. C32 | #15688531 | direct (N × H) |
| 99. C3 | C3×#15688531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688531 | 3 |
| C32×#11758608 | 3 |
| C32×#11758605 | 3 |
| C32×#11758606 | 3 |
| C32×C32⋊(C37⋊C3) | 3 |
| C32×C9×C37⋊C3 | 3 |
| C33×C9×C37 | 3 |
| C32×#737 | 37 |