Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
432 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 70 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. #22582572 | C3 | semidirect |
| 3. #22582559 | C3 | semidirect |
| 4. #22582480 | C3 | semidirect |
| 5. #22582477 | C3 | semidirect |
| 6. #22582468 | C3 | semidirect |
| 7. C33×C9×C37 | C3 | semidirect |
| 27. C33×C37 | 3−1+2 | semidirect |
| 61. C9×C37 | AΣL(1,𝔽27) | semidirect |
| 65. C33×C9 | C37⋊C3 | semidirect |
| 94. C37 | #10624784 | semidirect |
| 100. C33 | #11758606 | semidirect |
| 135. C9 | #15688513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688513 | 3 |
| #22582572 | 3 |
| #22582559 | 3 |
| #22582480 | 3 |
| #22582477 | 3 |
| #22582468 | 3 |
| C33×C9×C37 | 3 |
| #10624784 | 37 |