Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
476 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 108 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. #22582693 | C3 | direct (N × H) |
| 8. C32×#66524 | C9 | semidirect |
| 13. C3×C9×C37⋊C3 | C9 | semidirect |
| 15. C32×C9×C37 | C9 | semidirect |
| 29. C3×C9×C37 | C3×C9 | semidirect |
| 32. C3×#66524 | C3×C9 | semidirect |
| 63. C3×C37 | #6868 | semidirect |
| 67. C37⋊C3 | #6868 | semidirect |
| 79. C32×C9 | #66526 | semidirect |
| 82. C37 | C3×#6868 | semidirect |
| 103. C3×C9 | C3×#66526 | semidirect |
| 131. C3 | #22582693 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊#66526 | 3 |
| #22582693 | 3 |
| C32×C9×C37⋊C3 | 3 |
| C3×#6868 | 37 |