Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1688 conjugacy classes of subgroups; only the 468 normal subgroups are shown.
This group has 1688 conjugacy classes of subgroups — too many to draw. Only its 468 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. C33×#66526 | C3 | semidirect |
| 2. H(3,𝔽3)×#66526 | C3 | direct (N × H) |
| 3. C3×C32⋊#66526 | C3 | semidirect |
| 8. C32×#66526 | C32 | semidirect |
| 9. C32⋊#66526 | C32 | semidirect |
| 11. C3×C32⋊(C37⋊C3) | C9 | semidirect |
| 12. H(3,𝔽3)×C37⋊C3 | C9 | semidirect |
| 14. C3×H(3,𝔽3)×C37 | C9 | semidirect |
| 15. C33×C37 | C3×C9 | semidirect |
| 18. C32×C37⋊C3 | C3×C9 | semidirect |
| 19. C32×C37⋊C3 | C3×C9 | semidirect |
| 24. C3×#66526 | H(3,𝔽3) | direct (N × H) |
| 27. H(3,𝔽3)×C37 | C3×C9 | semidirect |
| 28. C32⋊(C37⋊C3) | C3×C9 | semidirect |
| 32. C32×C37 | C32×C9 | semidirect |
| 38. C3×C37⋊C3 | C32×C9 | semidirect |
| 43. #66526 | C3×H(3,𝔽3) | direct (N × H) |
| 49. C3×C37 | C9×H(3,𝔽3) | semidirect |
| 52. C37⋊C3 | C9×H(3,𝔽3) | semidirect |
| 59. C3×H(3,𝔽3) | #66526 | direct (N × H) |
| 65. C37 | C3×C9×H(3,𝔽3) | semidirect |
| 72. C33 | C3×#66526 | semidirect |
| 74. H(3,𝔽3) | C3×#66526 | direct (N × H) |
| 91. C32 | C32×#66526 | semidirect |
| 99. C3 | H(3,𝔽3)×#66526 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66526 | 3 |
| H(3,𝔽3)×#66526 | 3 |
| C3×C32⋊#66526 | 3 |
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| C3×C9×H(3,𝔽3) | 37 |