Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
410 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 139 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×#15688506 | C3 | semidirect |
| 2. C3×#15688505 | C3 | semidirect |
| 5. C3×C9×#66524 | C3 | semidirect |
| 6. #22582441 | C3 | semidirect |
| 7. #22582441 | C3 | semidirect |
| 8. #22582441 | C3 | semidirect |
| 24. C37×C32⋊C9 | C9 | semidirect |
| 124. C32⋊C9 | #66524 | semidirect |
| 126. C37 | #10624557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688506 | 3 |
| C3×#15688505 | 3 |
| C3×C32⋊#66524 | 3 |
| C3×C9×#66524 | 3 |
| #22582441 | 3 |
| C3×C37×C32⋊C9 | 3 |
| #10624557 | 37 |