Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
224 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 224 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. #22582612 | C3 | semidirect |
| 3. #22582487 | C3 | semidirect |
| 4. #22582484 | C3 | semidirect |
| 5. #22582474 | C3 | semidirect |
| 6. C32×C27×C37 | C3 | semidirect |
| 54. C32×C27 | C37⋊C3 | semidirect |
| 78. C37 | #10624724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582633 | 3 |
| #22582612 | 3 |
| #22582487 | 3 |
| #22582484 | 3 |
| #22582474 | 3 |
| C32×C27×C37 | 3 |
| #10624724 | 37 |