Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
328 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 88 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. C9×C32⋊(C37⋊C3) | C3 | semidirect |
| 3. #22582477 | C3 | semidirect |
| 4. #22582472 | C3 | semidirect |
| 5. C3×C92×C37 | C3 | semidirect |
| 8. #15688519 | C9 | direct (N × H) |
| 23. C3×C9×C37 | C3×C9 | semidirect |
| 27. C32⋊(C37⋊C3) | C3×C9 | semidirect |
| 42. C9×C37 | #732 | semidirect |
| 46. C3×C92 | C37⋊C3 | semidirect |
| 65. C37 | C9×#732 | semidirect |
| 77. C3×C9 | C9×C37⋊C3 | semidirect |
| 92. C9 | #15688519 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688519 | 3 |
| C9×C32⋊(C37⋊C3) | 3 |
| #22582477 | 3 |
| #22582472 | 3 |
| C3×C92×C37 | 3 |
| C9×#732 | 37 |