Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
236 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 236 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. #22582568 | C3 | semidirect |
| 3. 3−1+2×#66524 | C3 | semidirect |
| 4. C3×#15688504 | 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 |
| 11. #22582470 | C3 | semidirect |
| 12. #22582470 | C3 | semidirect |
| 45. 3−1+2×C37 | 3−1+2 | semidirect |
| 92. #66524 | #731 | semidirect |
| 139. C37 | #10624800 | semidirect |
| 146. 3−1+2 | #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 |
| 3−1+2×#66524 | 3 |
| C3×#15688504 | 3 |
| 3−1+2⋊#66524 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582470 | 3 |
| C3×C37×#731 | 3 |
| #10624800 | 37 |