Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22582539 | C3 | semidirect |
| 3. C3×#15688506 | C3 | semidirect |
| 4. #22582475 | C3 | semidirect |
| 5. #22582472 | C3 | semidirect |
| 6. C37×#6868 | C3 | semidirect |
| 11. #15688519 | C9 | semidirect |
| 22. C3×C9×C37 | C3×C9 | semidirect |
| 24. C32⋊(C37⋊C3) | C3×C9 | semidirect |
| 50. #6868 | C37⋊C3 | semidirect |
| 67. C37 | #10624722 | semidirect |
| 81. C3×C9 | C9×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688519 | 3 |
| #22582539 | 3 |
| C3×#15688506 | 3 |
| #22582475 | 3 |
| #22582472 | 3 |
| C37×#6868 | 3 |
| #10624722 | 37 |