Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1052 conjugacy classes of subgroups; only the 450 normal subgroups are shown.
This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 450 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. #22582722 | C3 | direct (N × H) |
| 2. C3×#15688538 | C3 | semidirect |
| 3. C3×#15688537 | C3 | semidirect |
| 5. C3×C9×#66526 | C3 | semidirect |
| 8. #15688538 | C32 | semidirect |
| 9. #15688537 | C32 | semidirect |
| 11. C9×#66526 | C32 | semidirect |
| 13. C32×#66524 | C9 | semidirect |
| 14. C3×C9×C37⋊C3 | C9 | semidirect |
| 15. C3×C9×C37⋊C3 | C9 | semidirect |
| 16. C3×C9×C37⋊C3 | C9 | semidirect |
| 17. C3×C9×C37⋊C3 | C9 | semidirect |
| 22. C32×C9×C37 | C9 | semidirect |
| 34. C3×C9×C37 | C3×C9 | semidirect |
| 38. C3×#66524 | C3×C9 | semidirect |
| 42. C9×C37⋊C3 | C3×C9 | semidirect |
| 43. C9×C37⋊C3 | C3×C9 | semidirect |
| 44. C9×C37⋊C3 | C3×C9 | semidirect |
| 73. C3×C37 | #6887 | semidirect |
| 76. C37⋊C3 | #6887 | semidirect |
| 89. C32×C9 | #66526 | semidirect |
| 94. C37 | C3×#6887 | semidirect |
| 119. C3×C9 | C3×#66526 | semidirect |
| 141. C3 | #22582722 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582722 | 3 |
| C3×#15688538 | 3 |
| C3×#15688537 | 3 |
| C3×C32⋊#66526 | 3 |
| C3×C9×#66526 | 3 |
| C32×C9×C37⋊C3 | 3 |
| C3×#6887 | 37 |