Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
164 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 7. #15688511 | C9 | semidirect |
| 12. C3×#11758601 | C9 | semidirect |
| 20. C37×C27⋊C3 | C9 | semidirect |
| 70. C27⋊C3 | #66524 | semidirect |
| 81. C37 | #10624468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688511 | 3 |
| C32×#11758601 | 3 |
| #22582538 | 3 |
| C3×C37×C27⋊C3 | 3 |
| #10624468 | 37 |