Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
620 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 256 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. #22582593 | C3 | semidirect |
| 2. #22582590 | C3 | semidirect |
| 3. #22582568 | C3 | semidirect |
| 5. 3−1+2×#66524 | C3 | semidirect |
| 11. #15688506 | C32 | semidirect |
| 12. #15688505 | C32 | semidirect |
| 13. #15688504 | C32 | semidirect |
| 19. C9×#66524 | C32 | semidirect |
| 84. C37 | #10624890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582593 | 3 |
| #22582590 | 3 |
| #22582568 | 3 |
| #22582554 | 3 |
| 3−1+2×#66524 | 3 |
| C3×C32⋊#66524 | 3 |
| C37×#6891 | 3 |
| #10624890 | 37 |