Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
284 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 284 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 |
|---|---|---|
| 4. #22582488 | C3 | direct (N × H) |
| 26. C3×#66524 | C27 | semidirect |
| 45. #66524 | C3×C27 | semidirect |
| 51. C3×C37 | C9⋊C27 | semidirect |
| 68. C37 | C3×C9⋊C27 | semidirect |
| 96. C3 | #22582488 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#11758601 | 3 |
| C3×C9×#66524 | 3 |
| #22582488 | 3 |
| C32×C27×C37 | 3 |
| C3×C9⋊C27 | 37 |