Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 7. #15688543 | C9 | semidirect |
| 13. (C37⋊C3)⋊C27 | C9 | semidirect |
| 18. #15688511 | C9 | semidirect |
| 22. C37×C27⋊C3 | C9 | semidirect |
| 78. C27⋊C3 | #66526 | semidirect |
| 85. C37 | #10624472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C37⋊C3)⋊(C27⋊C3) | 3 |
| C3×#15688537 | 3 |
| C27⋊C3×C37⋊C3 | 3 |
| #10624472 | 37 |