Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
416 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 87 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. (C37⋊C3)⋊(C27⋊C3) | C3 | semidirect |
| 2. #22582696 | C3 | semidirect |
| 3. #22582695 | C3 | semidirect |
| 4. #22582694 | C3 | semidirect |
| 8. #15688541 | C32 | semidirect |
| 134. C37⋊C3 | #6869 | semidirect |
| 161. C37 | C3×#6869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C37⋊C3)⋊(C27⋊C3) | 3 |
| #22582696 | 3 |
| #22582695 | 3 |
| #22582694 | 3 |
| C32×C9×C37⋊C3 | 3 |
| C3×#6869 | 37 |