Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
314 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 314 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. #22582553 | C3 | semidirect |
| 3. C3×#15688502 | C3 | semidirect |
| 4. C32⋊C9×C37⋊C3 | C3 | semidirect |
| 5. #22582477 | C3 | semidirect |
| 6. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 7. #22582475 | C3 | semidirect |
| 8. #22582475 | C3 | semidirect |
| 9. C37×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 102. H(3,𝔽3)⋊C9 | C37⋊C3 | semidirect |
| 135. C37 | #10624820 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582553 | 3 |
| (C3×C37⋊C3)⋊H(3,𝔽3) | 3 |
| C3×#15688502 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| #22582477 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582475 | 3 |
| C37×H(3,𝔽3)⋊C9 | 3 |
| #10624820 | 37 |