Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
192 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22582488 | C3 | semidirect |
| 3. #22582488 | C3 | semidirect |
| 4. #22582488 | C3 | semidirect |
| 6. #22582463 | C3 | semidirect |
| 7. #22582462 | C3 | semidirect |
| 8. C27×#66524 | C3 | semidirect |
| 38. C27×C37 | 3−1+2 | semidirect |
| 55. #66524 | C27⋊C3 | semidirect |
| 84. C37 | #10624728 | semidirect |
| 101. C27 | #11758608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#11758608 | 3 |
| #22582488 | 3 |
| C32⋊#11758601 | 3 |
| #22582463 | 3 |
| #22582462 | 3 |
| C27×#66524 | 3 |
| C3×C37×C27⋊C3 | 3 |
| #10624728 | 37 |