Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
2996 conjugacy classes of subgroups; only the 814 normal subgroups are shown.
This group has 2996 conjugacy classes of subgroups — too many to draw. Only its 814 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 |
|---|---|---|
| 2. C33×#66524 | C3 | semidirect |
| 3. C3×#15688502 | C3 | direct (N × H) |
| 4. C33×C9×C37 | C3 | semidirect |
| 8. C33×C37⋊C3 | C9 | semidirect |
| 11. C32×#66524 | C32 | semidirect |
| 12. #15688502 | C32 | direct (N × H) |
| 15. C32×C9×C37 | C32 | semidirect |
| 25. C32×C37⋊C3 | C3×C9 | semidirect |
| 28. C3×C9×C37 | C33 | semidirect |
| 30. C3×#66524 | C33 | semidirect |
| 32. C32×C37 | C32⋊C9 | semidirect |
| 42. C3×C37⋊C3 | C32×C9 | semidirect |
| 47. C33×C9 | C37⋊C3 | semidirect |
| 49. C3×C37 | C3×C32⋊C9 | semidirect |
| 64. C32×C9 | C3×C37⋊C3 | semidirect |
| 66. C37 | C32×C32⋊C9 | semidirect |
| 81. C3×C9 | C32×C37⋊C3 | semidirect |
| 87. C32 | #15688502 | direct (N × H) |
| 96. C3 | C3×#15688502 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C34×C37⋊C3 | 3 |
| C33×#66524 | 3 |
| C3×#15688502 | 3 |
| C33×C9×C37 | 3 |
| C32×C32⋊C9 | 37 |