Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
530 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 67 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. C33×#66524 | C3 | semidirect |
| 2. C3×#15688520 | C3 | semidirect |
| 3. C3×#15688518 | C3 | semidirect |
| 4. C3×#15688517 | C3 | semidirect |
| 5. C3×#15688515 | C3 | semidirect |
| 6. C3×#15688513 | C3 | semidirect |
| 7. #22582565 | C3 | semidirect |
| 8. #22582562 | C3 | semidirect |
| 9. C3×C37×AΣL(1,𝔽27) | C3 | semidirect |
| 97. C3×AΣL(1,𝔽27) | C37⋊C3 | semidirect |
| 129. C37 | #10624734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#66524 | 3 |
| C3×#15688520 | 3 |
| C3×#15688518 | 3 |
| C3×#15688517 | 3 |
| C3×#15688515 | 3 |
| C3×#15688513 | 3 |
| #22582565 | 3 |
| #22582562 | 3 |
| C3×C37×AΣL(1,𝔽27) | 3 |
| #10624734 | 37 |