Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
554 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 129 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×#15688537 | C3 | semidirect |
| 3. (C3×#66526)⋊C9 | C3 | semidirect |
| 9. C32×#66524 | C9 | semidirect |
| 12. C3×C9×C37⋊C3 | C9 | semidirect |
| 13. C3×C9×C37⋊C3 | C9 | semidirect |
| 16. C32×C9×C37 | C9 | semidirect |
| 42. C32×C37 | C9⋊C9 | semidirect |
| 48. C3×C37⋊C3 | C9⋊C9 | semidirect |
| 55. C9×C37 | C32⋊C9 | semidirect |
| 57. #66524 | C32⋊C9 | semidirect |
| 78. C32×C9 | #66526 | semidirect |
| 81. C37 | #10624548 | semidirect |
| 115. C32 | #15688537 | semidirect |
| 121. C9 | C32⋊#66526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688537 | 3 |
| C3×C32⋊#66526 | 3 |
| (C3×#66526)⋊C9 | 3 |
| C32×C9×C37⋊C3 | 3 |
| #10624548 | 37 |