Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1052 conjugacy classes of subgroups; only the 342 normal subgroups are shown.
This group has 1052 conjugacy classes of subgroups — too many to draw. Only its 342 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×#66526)⋊C9 | C3 | direct (N × H) |
| 7. C32×#66526 | C9 | semidirect |
| 10. C32×#66524 | C9 | semidirect |
| 13. C3×C9×C37⋊C3 | C9 | semidirect |
| 15. C32×C9×C37 | C9 | semidirect |
| 28. C3×#66526 | C3×C9 | semidirect |
| 30. C3×C9×C37 | C3×C9 | semidirect |
| 32. C3×#66524 | C3×C9 | semidirect |
| 59. C3×C37 | #6855 | semidirect |
| 64. C37⋊C3 | #6855 | semidirect |
| 78. C32×C9 | #66526 | semidirect |
| 79. C37 | C3×#6855 | semidirect |
| 99. C3×C9 | C3×#66526 | semidirect |
| 122. C3 | (C3×#66526)⋊C9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66526 | 3 |
| (C3×#66526)⋊C9 | 3 |
| C32×C9×C37⋊C3 | 3 |
| C3×#6855 | 37 |