Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1688 conjugacy classes of subgroups; only the 508 normal subgroups are shown.
This group has 1688 conjugacy classes of subgroups — too many to draw. Only its 508 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 |
|---|---|---|
| 2. C33×#66524 | C3 | semidirect |
| 3. C32×C9×C37⋊C3 | C3 | semidirect |
| 4. #22582539 | C3 | direct (N × H) |
| 5. C3×C32⋊#66524 | C3 | semidirect |
| 6. C3×#15688502 | C3 | semidirect |
| 7. C3×C37×C32⋊C9 | C3 | semidirect |
| 9. C3×C32⋊(C37⋊C3) | C9 | semidirect |
| 15. C32×#66524 | C32 | semidirect |
| 17. C3×C9×C37⋊C3 | C32 | semidirect |
| 18. C32⋊#66524 | C32 | semidirect |
| 19. #15688502 | C32 | semidirect |
| 22. C37×C32⋊C9 | C32 | semidirect |
| 25. C33×C37 | C3×C9 | semidirect |
| 30. C32×C37⋊C3 | C3×C9 | semidirect |
| 34. C32⋊(C37⋊C3) | C3×C9 | semidirect |
| 38. C3×#66524 | H(3,𝔽3) | semidirect |
| 48. C32×C37 | C32×C9 | semidirect |
| 55. C3×C37⋊C3 | C32×C9 | semidirect |
| 59. #66524 | C3×H(3,𝔽3) | semidirect |
| 66. C3×C32⋊C9 | C37⋊C3 | semidirect |
| 68. C3×C37 | C9×H(3,𝔽3) | semidirect |
| 87. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 88. C37 | C3×C9×H(3,𝔽3) | semidirect |
| 95. C33 | C9×C37⋊C3 | semidirect |
| 117. C32 | C3×C9×C37⋊C3 | semidirect |
| 127. C3 | #22582539 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C32⋊(C37⋊C3) | 3 |
| C33×#66524 | 3 |
| C32×C9×C37⋊C3 | 3 |
| #22582539 | 3 |
| C3×C32⋊#66524 | 3 |
| C3×#15688502 | 3 |
| C3×C37×C32⋊C9 | 3 |
| C3×C9×H(3,𝔽3) | 37 |