Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
926 conjugacy classes of subgroups; only the 292 normal subgroups are shown.
This group has 926 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 |
|---|---|---|
| 2. #22582560 | C3 | semidirect |
| 3. #22582559 | C3 | semidirect |
| 4. #22582552 | C3 | semidirect |
| 5. C3×C32⋊#66524 | C3 | semidirect |
| 6. C3×C37×C32⋊C9 | C3 | semidirect |
| 8. C3×#11758606 | C32 | semidirect |
| 12. C32×#66524 | C32 | semidirect |
| 14. C32⋊#66524 | C32 | semidirect |
| 15. C32⋊#66524 | C32 | semidirect |
| 16. #15688502 | C32 | semidirect |
| 18. C32×C9×C37 | C32 | semidirect |
| 20. C37×C32⋊C9 | C32 | semidirect |
| 23. C33×C37 | 3−1+2 | semidirect |
| 61. C3×C32⋊C9 | C37⋊C3 | semidirect |
| 76. C32×C9 | C3×C37⋊C3 | semidirect |
| 82. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 83. C37 | #10624883 | semidirect |
| 90. C33 | #11758606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C37⋊C3) | 3 |
| #22582560 | 3 |
| #22582559 | 3 |
| #22582552 | 3 |
| C3×C32⋊#66524 | 3 |
| C3×C37×C32⋊C9 | 3 |
| #10624883 | 37 |