Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
2996 conjugacy classes of subgroups; only the 630 normal subgroups are shown.
This group has 2996 conjugacy classes of subgroups — too many to draw. Only its 630 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. C33×#66526 | C3 | semidirect |
| 2. C3×C32⋊#66526 | C3 | direct (N × H) |
| 5. C32×#66526 | C32 | semidirect |
| 6. C32⋊#66526 | C32 | direct (N × H) |
| 9. C33×C37⋊C3 | C9 | semidirect |
| 10. C33×C37⋊C3 | C9 | semidirect |
| 13. C34×C37 | C9 | semidirect |
| 16. C33×C37 | C3×C9 | semidirect |
| 22. C32×C37⋊C3 | C3×C9 | semidirect |
| 23. C32×C37⋊C3 | C3×C9 | semidirect |
| 29. C3×#66526 | C33 | semidirect |
| 32. C32×C37 | C32⋊C9 | semidirect |
| 34. C32×C37 | C32×C9 | semidirect |
| 39. C3×C37⋊C3 | C32⋊C9 | semidirect |
| 41. C3×C37⋊C3 | C32×C9 | semidirect |
| 50. C3×C37 | C3×C32⋊C9 | semidirect |
| 53. C37⋊C3 | C3×C32⋊C9 | semidirect |
| 62. C34 | #66526 | semidirect |
| 66. C37 | C32×C32⋊C9 | semidirect |
| 80. C33 | C3×#66526 | semidirect |
| 94. C32 | C32⋊#66526 | direct (N × H) |
| 96. C32 | C32×#66526 | semidirect |
| 103. C3 | C3×C32⋊#66526 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66526 | 3 |
| C3×C32⋊#66526 | 3 |
| C34×C37⋊C3 | 3 |
| C32×C32⋊C9 | 37 |