Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
224 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 66 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. #22582731 | C3 | semidirect |
| 2. C3×(C37⋊C3)⋊C27 | C3 | semidirect |
| 3. #22582701 | C3 | semidirect |
| 4. #22582699 | C3 | semidirect |
| 5. #22582695 | C3 | semidirect |
| 70. C37 | #10624724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582731 | 3 |
| C3×(C37⋊C3)⋊C27 | 3 |
| #22582701 | 3 |
| #22582699 | 3 |
| #22582695 | 3 |
| #22582631 | 3 |
| #10624724 | 37 |