Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
554 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 166 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. C3×#15688504 | C3 | semidirect |
| 5. #22582441 | C3 | semidirect |
| 9. C32×#66524 | C9 | semidirect |
| 55. C32×C37 | C9⋊C9 | semidirect |
| 69. #66524 | C32⋊C9 | semidirect |
| 99. C37 | #10624548 | semidirect |
| 134. C32 | #15688504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66524 | 3 |
| C3×#15688504 | 3 |
| C3×C32⋊#66524 | 3 |
| #22582441 | 3 |
| C3×C37×C32⋊C9 | 3 |
| #10624548 | 37 |