Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
292 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 72 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. C3×C9×#66526 | C3 | semidirect |
| 4. 3−1+2⋊#66526 | C3 | semidirect |
| 6. #22582692 | C3 | semidirect |
| 22. #15688517 | C9 | semidirect |
| 23. #15688516 | C9 | semidirect |
| 24. #15688515 | C9 | semidirect |
| 25. C37×#731 | C9 | semidirect |
| 36. 3−1+2×C37 | C3×C9 | semidirect |
| 38. C3×C9×C37 | C3×C9 | semidirect |
| 41. #11758608 | C3×C9 | semidirect |
| 42. C3×#66524 | C3×C9 | semidirect |
| 62. #66526 | #731 | direct (N × H) |
| 90. #731 | #66526 | direct (N × H) |
| 99. C37 | C9×#731 | semidirect |
| 105. 3−1+2 | C3×#66526 | semidirect |
| 121. 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 |
| C3×C9×#66526 | 3 |
| 3−1+2⋊#66526 | 3 |
| H(3,𝔽3)⋊#66526 | 3 |
| #22582692 | 3 |
| #731×C37⋊C3 | 3 |
| C9×#731 | 37 |