Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
602 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 256 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. #22582593 | C3 | semidirect |
| 2. #22582590 | C3 | semidirect |
| 3. #22582585 | C3 | semidirect |
| 4. #22582579 | C3 | semidirect |
| 5. #22582578 | C3 | semidirect |
| 6. #22582575 | C3 | semidirect |
| 7. #22582573 | C3 | semidirect |
| 8. #22582568 | C3 | semidirect |
| 9. #22582568 | C3 | semidirect |
| 11. 3−1+2×#66524 | C3 | semidirect |
| 12. 3−1+2×#66524 | C3 | semidirect |
| 14. C3×#15688506 | C3 | semidirect |
| 154. C37 | #10624891 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582593 | 3 |
| #22582590 | 3 |
| #22582585 | 3 |
| #22582579 | 3 |
| #22582578 | 3 |
| #22582575 | 3 |
| #22582573 | 3 |
| #22582568 | 3 |
| #22582556 | 3 |
| 3−1+2×#66524 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| C3×#15688506 | 3 |
| C37×#6893 | 3 |
| #10624891 | 37 |