Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
172 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 76 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. #22582490 | C3 | semidirect |
| 3. #22582489 | C3 | semidirect |
| 4. #22582488 | C3 | semidirect |
| 5. #22582488 | C3 | semidirect |
| 6. #22582488 | C3 | semidirect |
| 10. #22582463 | C3 | semidirect |
| 11. #22582462 | C3 | semidirect |
| 12. C27×#66524 | C3 | semidirect |
| 13. C37×C9⋊C27 | C3 | semidirect |
| 74. C9⋊C27 | C37⋊C3 | semidirect |
| 103. C37 | #10624712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582536 | 3 |
| #22582490 | 3 |
| #22582489 | 3 |
| #22582488 | 3 |
| #22582465 | 3 |
| #22582463 | 3 |
| #22582462 | 3 |
| C27×#66524 | 3 |
| C37×C9⋊C27 | 3 |
| #10624712 | 37 |