Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
512 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 2. C3×#15688502 | C3 | semidirect |
| 3. C32⋊C9×C37⋊C3 | C3 | semidirect |
| 4. #22582477 | C3 | semidirect |
| 5. H(3,𝔽3)⋊#66524 | C3 | semidirect |
| 6. #22582475 | C3 | semidirect |
| 7. C37×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 13. H(3,𝔽3)×C37⋊C3 | C9 | semidirect |
| 14. C32×#66524 | C32 | semidirect |
| 16. C32⋊#66524 | C32 | semidirect |
| 22. C32×C9×C37 | C32 | semidirect |
| 23. C37×C32⋊C9 | C32 | semidirect |
| 39. H(3,𝔽3)×C37 | C3×C9 | semidirect |
| 45. C32⋊(C37⋊C3) | C3×C9 | semidirect |
| 86. H(3,𝔽3)⋊C9 | C37⋊C3 | semidirect |
| 106. C32×C9 | C3×C37⋊C3 | semidirect |
| 112. C32⋊C9 | C3×C37⋊C3 | semidirect |
| 113. C37 | #10624698 | semidirect |
| 132. H(3,𝔽3) | C9×C37⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| C3×#15688502 | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| #22582477 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582475 | 3 |
| C37×H(3,𝔽3)⋊C9 | 3 |
| #10624698 | 37 |