Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
206 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 206 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. #22582488 | C3 | semidirect |
| 4. #22582463 | C3 | semidirect |
| 66. C37 | #10624711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#66524 | 3 |
| #22582488 | 3 |
| C32⋊#11758601 | 3 |
| #22582463 | 3 |
| C37×C32⋊C27 | 3 |
| #10624711 | 37 |