Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
980 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 271 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 |
|---|---|---|
| 3. #22582652 | C3 | semidirect |
| 4. #22582651 | C3 | semidirect |
| 5. #22582650 | C3 | semidirect |
| 6. #22582649 | C3 | semidirect |
| 7. #733×C37⋊C3 | C3 | semidirect |
| 8. C37×#6912 | C3 | semidirect |
| 30. #15688521 | C32 | semidirect |
| 31. #15688520 | C32 | semidirect |
| 34. C37×#733 | C32 | semidirect |
| 94. #6912 | C37⋊C3 | direct (N × H) |
| 103. C37⋊C3 | #6912 | direct (N × H) |
| 129. #733 | C3×C37⋊C3 | semidirect |
| 130. C37 | C3×#6912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C37⋊C3 | 3 |
| #22582652 | 3 |
| #22582651 | 3 |
| #22582650 | 3 |
| #22582649 | 3 |
| #733×C37⋊C3 | 3 |
| C37×#6912 | 3 |
| C3×#6912 | 37 |