Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
172 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22582706 | C3 | semidirect |
| 2. #22582705 | C3 | semidirect |
| 3. #22582704 | C3 | semidirect |
| 4. #22582703 | C3 | semidirect |
| 7. #22582688 | C3 | semidirect |
| 8. C9×#11758603 | C3 | semidirect |
| 81. C37 | #10624713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582706 | 3 |
| #22582705 | 3 |
| #22582704 | 3 |
| #22582703 | 3 |
| C32⋊#11758603 | 3 |
| #22582688 | 3 |
| C9×#11758603 | 3 |
| #22582535 | 3 |
| #10624713 | 37 |