Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
560 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 55 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. C3×3−1+2×C37⋊C3 | C3 | semidirect |
| 3. #22582552 | C3 | semidirect |
| 4. #22582551 | C3 | semidirect |
| 5. #22582446 | C3 | semidirect |
| 6. #22582445 | C3 | semidirect |
| 7. #22582444 | C3 | semidirect |
| 8. #22582444 | C3 | semidirect |
| 9. C37×#6857 | C3 | semidirect |
| 12. C3×#11758608 | C32 | semidirect |
| 13. C3×#11758608 | C32 | semidirect |
| 23. C32⋊#66524 | C32 | semidirect |
| 29. C3×3−1+2×C37 | C32 | semidirect |
| 30. C3×3−1+2×C37 | C32 | semidirect |
| 32. C37×C32⋊C9 | C32 | semidirect |
| 107. #6857 | C37⋊C3 | semidirect |
| 126. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 127. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 140. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 141. C37 | #10624590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×3−1+2×C37⋊C3 | 3 |
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| #22582552 | 3 |
| #22582551 | 3 |
| #22582446 | 3 |
| #22582445 | 3 |
| #22582444 | 3 |
| C37×#6857 | 3 |
| #10624590 | 37 |