Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1148 conjugacy classes of subgroups; only the 295 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 295 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×#15688530 | C3 | semidirect |
| 3. #22582565 | C3 | semidirect |
| 4. #22582564 | C3 | semidirect |
| 5. #22582551 | C3 | semidirect |
| 6. C3×#15688502 | C3 | semidirect |
| 7. C3×C37×#737 | C3 | semidirect |
| 10. C3×#11758608 | C32 | semidirect |
| 13. C32×#66524 | C32 | semidirect |
| 16. #15688502 | C32 | semidirect |
| 17. #15688502 | C32 | semidirect |
| 18. #15688502 | C32 | semidirect |
| 20. C3×3−1+2×C37 | C32 | semidirect |
| 22. C32×C9×C37 | C32 | semidirect |
| 54. C3×C37⋊C3 | #737 | semidirect |
| 60. C3×#737 | C37⋊C3 | semidirect |
| 77. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 82. C32×C9 | C3×C37⋊C3 | semidirect |
| 88. C37 | #10624894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688530 | 3 |
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| #22582565 | 3 |
| #22582564 | 3 |
| #22582551 | 3 |
| C3×#15688502 | 3 |
| C3×C37×#737 | 3 |
| #10624894 | 37 |