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. #22582661 | C3 | direct (N × H) |
| 3. C3×#15688521 | C3 | semidirect |
| 4. C3×#15688519 | C3 | semidirect |
| 5. C3×#15688516 | C3 | semidirect |
| 6. C3×#15688513 | C3 | semidirect |
| 7. C32×3−1+2×C37 | C3 | semidirect |
| 9. #15688531 | C32 | semidirect |
| 15. #15688521 | C32 | semidirect |
| 16. #15688519 | C32 | semidirect |
| 17. #15688516 | C32 | semidirect |
| 18. #15688513 | C32 | semidirect |
| 22. C3×3−1+2×C37 | C32 | semidirect |
| 66. C32×3−1+2 | C37⋊C3 | semidirect |
| 75. C3×C37 | #6913 | semidirect |
| 86. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 96. C37 | C3×#6913 | semidirect |
| 139. C3 | #22582661 | 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 |
| #22582661 | 3 |
| C3×#15688521 | 3 |
| C3×#15688519 | 3 |
| C3×#15688516 | 3 |
| C3×#15688513 | 3 |
| C32×3−1+2×C37 | 3 |
| C3×#6913 | 37 |