Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
456 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 1. C37⋊H(5,𝔽3) | C3 | semidirect |
| 2. #22582642 | C3 | semidirect |
| 3. #22582638 | C3 | semidirect |
| 4. #22582637 | C3 | semidirect |
| 5. C3×#15688516 | C3 | semidirect |
| 6. #22582564 | C3 | semidirect |
| 7. C3×C37×#732 | C3 | semidirect |
| 8. C3×#11758608 | C32 | semidirect |
| 9. C3×#11758608 | C32 | semidirect |
| 21. C3×H(3,𝔽3)×C37 | C32 | semidirect |
| 22. C32×C9×C37 | C32 | semidirect |
| 71. C3×#732 | C37⋊C3 | semidirect |
| 90. C3×H(3,𝔽3) | C3×C37⋊C3 | semidirect |
| 91. C32×C9 | C3×C37⋊C3 | semidirect |
| 98. C37 | #10624748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37⋊H(5,𝔽3) | 3 |
| #22582642 | 3 |
| #22582638 | 3 |
| #22582637 | 3 |
| C3×#15688516 | 3 |
| #22582564 | 3 |
| C3×C37×#732 | 3 |
| #10624748 | 37 |