Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
268 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 82 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. C9×#11758608 | C3 | semidirect |
| 3. C3×#15688504 | C3 | semidirect |
| 4. #22582481 | C3 | semidirect |
| 5. #22582481 | C3 | semidirect |
| 8. #22582469 | C3 | semidirect |
| 14. #15688515 | C9 | semidirect |
| 37. #11758608 | C3×C9 | semidirect |
| 47. C3×#66524 | C3×C9 | semidirect |
| 101. C37 | #731⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688515 | 3 |
| C9×#11758608 | 3 |
| C3×#15688504 | 3 |
| #22582481 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| #22582469 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| #731⋊C9 | 37 |