Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
758 conjugacy classes of subgroups; only the 301 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 301 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. #22582601 | C3 | semidirect |
| 2. #22582594 | C3 | semidirect |
| 3. #22582580 | C3 | semidirect |
| 4. #22582568 | C3 | semidirect |
| 6. C9×#11758608 | C3 | semidirect |
| 7. #22582538 | C3 | semidirect |
| 8. #22582538 | C3 | semidirect |
| 9. C3×C9×#66524 | C3 | semidirect |
| 42. C3×C9×C37 | 3−1+2 | semidirect |
| 66. #66524 | #737 | semidirect |
| 105. C37 | #10624879 | semidirect |
| 119. C3×C9 | #11758608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582601 | 3 |
| #22582594 | 3 |
| #22582580 | 3 |
| #22582568 | 3 |
| #22582556 | 3 |
| C9×#11758608 | 3 |
| #22582538 | 3 |
| C3×C9×#66524 | 3 |
| C3×C37×#737 | 3 |
| #10624879 | 37 |