Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
334 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 334 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. C3×#15688531 | C3 | semidirect |
| 2. C9×#11758608 | C3 | semidirect |
| 3. #22582455 | C3 | semidirect |
| 4. #22582452 | C3 | semidirect |
| 5. #22582448 | C3 | semidirect |
| 6. #22582446 | C3 | semidirect |
| 7. #22582445 | C3 | semidirect |
| 9. C9×H(3,𝔽3)×C37 | C3 | semidirect |
| 72. C9×H(3,𝔽3) | C37⋊C3 | semidirect |
| 104. C37 | #10624583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688531 | 3 |
| C9×#11758608 | 3 |
| #22582455 | 3 |
| #22582452 | 3 |
| #22582448 | 3 |
| #22582446 | 3 |
| #22582445 | 3 |
| #22582442 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| #10624583 | 37 |