Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22582568 | C3 | semidirect |
| 2. #22582556 | C3 | semidirect |
| 3. C3×C32⋊#66524 | C3 | semidirect |
| 4. 3−1+2⋊#66524 | C3 | semidirect |
| 5. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 6. #22582468 | C3 | semidirect |
| 27. C33×C37 | 3−1+2 | semidirect |
| 90. C37 | #10624788 | semidirect |
| 96. C33 | #11758608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582568 | 3 |
| #22582556 | 3 |
| C3×C32⋊#66524 | 3 |
| 3−1+2⋊#66524 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582468 | 3 |
| C3×C37×AΣL(1,𝔽27) | 3 |
| #10624788 | 37 |