Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
334 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 52 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×#15688532 | C3 | semidirect |
| 2. #22582548 | C3 | semidirect |
| 3. 3−1+2×#66524 | C3 | semidirect |
| 4. H(3,𝔽3)×#66524 | C3 | semidirect |
| 5. #22582454 | C3 | semidirect |
| 6. #22582454 | C3 | semidirect |
| 7. #22582453 | C3 | semidirect |
| 8. #22582450 | C3 | semidirect |
| 9. #22582447 | C3 | semidirect |
| 10. #22582445 | C3 | semidirect |
| 11. #22582444 | C3 | semidirect |
| 13. C37×#6857 | C3 | semidirect |
| 105. #6857 | C37⋊C3 | semidirect |
| 140. C37 | #10624583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688532 | 3 |
| #22582548 | 3 |
| 3−1+2×#66524 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| #22582454 | 3 |
| #22582453 | 3 |
| #22582450 | 3 |
| #22582447 | 3 |
| #22582445 | 3 |
| #22582444 | 3 |
| #22582442 | 3 |
| C37×#6857 | 3 |
| #10624583 | 37 |