Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
280 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 64 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. #22582556 | C3 | semidirect |
| 2. C3×C9×#66524 | C3 | semidirect |
| 3. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 4. #22582472 | C3 | semidirect |
| 22. C3×C9×C37 | 3−1+2 | semidirect |
| 43. #66524 | #732 | semidirect |
| 65. C37 | #10624786 | semidirect |
| 79. C3×C9 | #11758608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582556 | 3 |
| C3×C9×#66524 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582472 | 3 |
| C3×C37×#732 | 3 |
| #10624786 | 37 |