Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
410 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 96 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×#15688538 | C3 | semidirect |
| 2. C3×#15688537 | C3 | semidirect |
| 5. C3×C9×#66526 | C3 | semidirect |
| 6. (C3×#66526)⋊C9 | C3 | semidirect |
| 7. (C3×#66526)⋊C9 | C3 | semidirect |
| 8. (C3×#66526)⋊C9 | C3 | semidirect |
| 24. C32⋊#66524 | C9 | semidirect |
| 25. #15688502 | C9 | semidirect |
| 26. #15688502 | C9 | semidirect |
| 27. #15688502 | C9 | semidirect |
| 28. C37×C32⋊C9 | C9 | semidirect |
| 143. C32⋊C9 | #66526 | semidirect |
| 145. C37 | #10624557 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688538 | 3 |
| C3×#15688537 | 3 |
| C3×C32⋊#66526 | 3 |
| C3×C9×#66526 | 3 |
| (C3×#66526)⋊C9 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| #10624557 | 37 |