Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
402 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22582652 | C3 | semidirect |
| 3. #22582651 | C3 | semidirect |
| 4. #22582651 | C3 | semidirect |
| 5. #22582651 | C3 | semidirect |
| 6. #22582651 | C3 | semidirect |
| 10. C3×#15688520 | C3 | semidirect |
| 11. C3×#15688520 | C3 | semidirect |
| 12. C3×#15688520 | C3 | semidirect |
| 13. C37×#6912 | C3 | semidirect |
| 137. #6912 | C37⋊C3 | semidirect |
| 187. C37 | #10624758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688532 | 3 |
| #22582652 | 3 |
| #22582651 | 3 |
| #22582644 | 3 |
| #22582643 | 3 |
| C3×#15688520 | 3 |
| C37×#6912 | 3 |
| #10624758 | 37 |