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. #22582647 | C3 | semidirect |
| 3. #22582647 | C3 | semidirect |
| 4. #22582639 | C3 | semidirect |
| 5. #22582638 | C3 | semidirect |
| 6. C3×#15688518 | C3 | semidirect |
| 7. C3×#15688517 | C3 | semidirect |
| 8. C3×#15688515 | C3 | semidirect |
| 9. C37×#6911 | C3 | semidirect |
| 10. C3×#11758608 | C32 | semidirect |
| 11. C3×#11758608 | C32 | semidirect |
| 15. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 18. C32×#66524 | C32 | semidirect |
| 26. C3×3−1+2×C37 | C32 | semidirect |
| 28. C3×H(3,𝔽3)×C37 | C32 | semidirect |
| 87. #6911 | C37⋊C3 | semidirect |
| 104. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 112. C3×H(3,𝔽3) | C3×C37⋊C3 | semidirect |
| 122. C37 | #10624760 | 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 |
| #22582647 | 3 |
| #22582639 | 3 |
| #22582638 | 3 |
| C3×#15688518 | 3 |
| C3×#15688517 | 3 |
| C3×#15688515 | 3 |
| C37×#6911 | 3 |
| #10624760 | 37 |