Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
572 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 73 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. C32×#11758608 | C3 | semidirect |
| 3. #22582554 | C3 | semidirect |
| 4. #22582475 | C3 | semidirect |
| 5. C37×#6891 | C3 | semidirect |
| 16. C32×#66524 | C32 | semidirect |
| 19. C32⋊#66524 | C32 | semidirect |
| 24. C37×C32⋊C9 | C32 | semidirect |
| 43. C32⋊(C37⋊C3) | 3−1+2 | semidirect |
| 81. #6891 | C37⋊C3 | semidirect |
| 110. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 111. C37 | #10624779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758608 | 3 |
| C32×C32⋊(C37⋊C3) | 3 |
| #22582554 | 3 |
| #22582475 | 3 |
| C37×#6891 | 3 |
| #10624779 | 37 |