Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
216 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 55 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. #22582575 | C3 | semidirect |
| 3. #22582535 | C3 | semidirect |
| 4. C3×#15688504 | C3 | semidirect |
| 5. #22582481 | C3 | semidirect |
| 6. #22582481 | C3 | semidirect |
| 7. #22582480 | C3 | semidirect |
| 8. #22582480 | C3 | semidirect |
| 9. #22582478 | C3 | semidirect |
| 10. #22582478 | C3 | semidirect |
| 126. C37 | #10624827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582575 | 3 |
| #22582562 | 3 |
| #22582535 | 3 |
| C3×#15688504 | 3 |
| #22582481 | 3 |
| #22582480 | 3 |
| #22582478 | 3 |
| H(3,𝔽3)⋊#66524 | 3 |
| C37×H(3,𝔽3)⋊C9 | 3 |
| #10624827 | 37 |