Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1988 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 1988 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 |
|---|---|---|
| 1. C3×C32⋊#66526 | C3 | semidirect |
| 2. #22582691 | C3 | direct (N × H) |
| 6. C32⋊#66526 | C32 | semidirect |
| 12. C33×C37⋊C3 | C9 | semidirect |
| 13. C33×C37⋊C3 | C9 | semidirect |
| 16. C34×C37 | C9 | semidirect |
| 21. C33×C37 | C3×C9 | semidirect |
| 37. C32×C37⋊C3 | C3×C9 | semidirect |
| 79. C3×C37 | #6866 | semidirect |
| 84. C37⋊C3 | #6866 | semidirect |
| 95. C34 | #66526 | semidirect |
| 99. C37 | C3×#6866 | semidirect |
| 125. C33 | C3×#66526 | semidirect |
| 163. C3 | #22582691 | 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 |
| #22582691 | 3 |
| C34×C37⋊C3 | 3 |
| C3×#6866 | 37 |