Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1304 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1304 conjugacy classes of subgroups — too many to draw. Only its 274 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. C32×#11758606 | C3 | semidirect |
| 2. C3×H(3,𝔽3)×C37⋊C3 | C3 | semidirect |
| 3. #22582646 | C3 | direct (N × H) |
| 4. C3×#15688519 | C3 | semidirect |
| 5. C3×#15688518 | C3 | semidirect |
| 6. C3×C37×#732 | C3 | semidirect |
| 11. C3×#11758606 | C32 | semidirect |
| 13. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 15. H(3,𝔽3)×C37⋊C3 | C32 | semidirect |
| 16. C32×#66524 | C32 | semidirect |
| 17. #15688519 | C32 | semidirect |
| 18. #15688518 | C32 | semidirect |
| 19. C3×H(3,𝔽3)×C37 | C32 | semidirect |
| 20. C32×C9×C37 | C32 | semidirect |
| 21. C37×#732 | C32 | semidirect |
| 32. H(3,𝔽3)×C37 | C33 | semidirect |
| 35. C3×C9×C37 | C33 | semidirect |
| 38. C32⋊(C37⋊C3) | C33 | semidirect |
| 41. C3×#66524 | C33 | semidirect |
| 64. C3×#732 | C37⋊C3 | semidirect |
| 68. C3×C37 | #6911 | semidirect |
| 81. C3×H(3,𝔽3) | C3×C37⋊C3 | semidirect |
| 83. C32×C9 | C3×C37⋊C3 | semidirect |
| 86. #732 | C3×C37⋊C3 | semidirect |
| 87. C37 | C3×#6911 | semidirect |
| 102. H(3,𝔽3) | C32×C37⋊C3 | semidirect |
| 108. C3×C9 | C32×C37⋊C3 | semidirect |
| 129. C3 | #22582646 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758606 | 3 |
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| #22582646 | 3 |
| C3×#15688519 | 3 |
| C3×#15688518 | 3 |
| C3×C37×#732 | 3 |
| C3×#6911 | 37 |