Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
758 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 286 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. #22582601 | C3 | semidirect |
| 3. #22582593 | C3 | semidirect |
| 4. #22582580 | C3 | semidirect |
| 5. #22582579 | C3 | semidirect |
| 6. #22582574 | C3 | semidirect |
| 7. #22582573 | C3 | semidirect |
| 8. #22582572 | C3 | semidirect |
| 9. #22582571 | C3 | semidirect |
| 11. #22582548 | C3 | semidirect |
| 12. 3−1+2×#66524 | C3 | semidirect |
| 13. #22582535 | C3 | semidirect |
| 14. C3×C9×#66524 | C3 | semidirect |
| 68. C3×#66524 | 3−1+2 | semidirect |
| 89. C9×C37 | #737 | semidirect |
| 99. #66524 | #737 | semidirect |
| 157. C37 | #10624879 | semidirect |
| 203. C9 | #15688530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688530 | 3 |
| #22582601 | 3 |
| #22582593 | 3 |
| #22582580 | 3 |
| #22582579 | 3 |
| #22582574 | 3 |
| #22582573 | 3 |
| #22582572 | 3 |
| #22582571 | 3 |
| #22582556 | 3 |
| #22582548 | 3 |
| 3−1+2×#66524 | 3 |
| #22582535 | 3 |
| C3×C9×#66524 | 3 |
| C37×C9⋊H(3,𝔽3) | 3 |
| #10624879 | 37 |