Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
230 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 8. C3×#11758601 | C9 | semidirect |
| 15. C3×C27×C37 | C9 | semidirect |
| 28. C3×#66524 | C27 | semidirect |
| 62. C3×C27 | #66524 | semidirect |
| 66. C37 | #10624463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758601 | 3 |
| C3×C9×#66524 | 3 |
| C32×C27×C37 | 3 |
| #10624463 | 37 |