Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
302 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 302 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. #22582552 | C3 | semidirect |
| 3. C32⋊C9×C37⋊C3 | C3 | semidirect |
| 4. C32⋊C9×C37⋊C3 | C3 | semidirect |
| 5. #22582453 | C3 | semidirect |
| 6. #22582453 | C3 | semidirect |
| 7. #22582452 | C3 | semidirect |
| 8. #22582451 | C3 | semidirect |
| 9. C37×#6859 | C3 | semidirect |
| 96. #6859 | C37⋊C3 | semidirect |
| 128. C37 | #10624598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582552 | 3 |
| (C3×C37⋊C3)⋊H(3,𝔽3) | 3 |
| C32⋊C9×C37⋊C3 | 3 |
| #22582453 | 3 |
| #22582452 | 3 |
| #22582451 | 3 |
| C37×#6859 | 3 |
| #10624598 | 37 |