Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
992 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 292 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. C3×#15688531 | C3 | semidirect |
| 2. C32×#11758605 | C3 | semidirect |
| 3. #22582655 | C3 | direct (N × H) |
| 4. C3×#15688520 | C3 | semidirect |
| 5. C3×#15688518 | C3 | semidirect |
| 6. C3×#15688517 | C3 | semidirect |
| 7. C3×#15688515 | C3 | semidirect |
| 8. C3×#15688514 | C3 | semidirect |
| 9. C3×#15688512 | C3 | semidirect |
| 10. C3×C37×#737 | C3 | semidirect |
| 13. #15688531 | C32 | semidirect |
| 20. C3×#11758605 | C32 | semidirect |
| 26. #15688520 | C32 | semidirect |
| 27. #15688518 | C32 | semidirect |
| 28. #15688517 | C32 | semidirect |
| 29. #15688515 | C32 | semidirect |
| 30. #15688514 | C32 | semidirect |
| 31. #15688512 | C32 | semidirect |
| 33. C37×#737 | C32 | semidirect |
| 97. C3×#737 | C37⋊C3 | semidirect |
| 109. C3×C37 | #6913 | semidirect |
| 117. #737 | C3×C37⋊C3 | semidirect |
| 141. C37 | C3×#6913 | semidirect |
| 203. C3 | #22582655 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688531 | 3 |
| C32×#11758605 | 3 |
| #22582655 | 3 |
| C3×#15688520 | 3 |
| C3×#15688518 | 3 |
| C3×#15688517 | 3 |
| C3×#15688515 | 3 |
| C3×#15688514 | 3 |
| C3×#15688512 | 3 |
| C3×C37×#737 | 3 |
| C3×#6913 | 37 |