Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
216 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 58 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. #22582578 | C3 | semidirect |
| 2. #22582538 | C3 | semidirect |
| 3. C3×#15688504 | C3 | semidirect |
| 4. 3−1+2⋊#66524 | C3 | semidirect |
| 5. 3−1+2⋊#66524 | C3 | semidirect |
| 6. 3−1+2⋊#66524 | C3 | semidirect |
| 7. 3−1+2⋊#66524 | C3 | semidirect |
| 8. 3−1+2⋊#66524 | C3 | semidirect |
| 9. 3−1+2⋊#66524 | C3 | semidirect |
| 130. C37 | #10624827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582578 | 3 |
| #22582538 | 3 |
| C3×#15688504 | 3 |
| 3−1+2⋊#66524 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| C37×#6893 | 3 |
| #10624827 | 37 |