Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
926 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 429 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. 3−1+2×#66526 | C3 | semidirect |
| 3. #22582722 | C3 | semidirect |
| 4. C3×#15688537 | C3 | semidirect |
| 13. #15688532 | C9 | semidirect |
| 14. #15688531 | C9 | semidirect |
| 15. #15688530 | C9 | semidirect |
| 19. C37×#737 | C9 | semidirect |
| 24. 3−1+2×C37 | C3×C9 | semidirect |
| 26. C3×C9×C37 | C3×C9 | semidirect |
| 28. #11758608 | C3×C9 | semidirect |
| 29. C3×#66524 | C3×C9 | semidirect |
| 30. #11758606 | C3×C9 | semidirect |
| 31. #11758605 | C3×C9 | semidirect |
| 32. C9×C37⋊C3 | C3×C9 | semidirect |
| 33. C9×C37⋊C3 | C3×C9 | semidirect |
| 59. #737 | #66526 | semidirect |
| 70. C37 | #10624864 | semidirect |
| 75. 3−1+2 | C3×#66526 | semidirect |
| 86. C3×C9 | C3×#66526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#66526 | 3 |
| H(3,𝔽3)×#66526 | 3 |
| #22582722 | 3 |
| C3×#15688537 | 3 |
| #737×C37⋊C3 | 3 |
| #10624864 | 37 |