Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1118 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 286 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. #22582680 | C3 | semidirect |
| 2. C37⋊H(5,𝔽3) | C3 | semidirect |
| 3. C3×H(3,𝔽3)×C37⋊C3 | C3 | semidirect |
| 4. #22582639 | C3 | semidirect |
| 5. C3×#15688514 | C3 | semidirect |
| 6. C37×3−1+4 | C3 | semidirect |
| 7. C33×C37⋊C3 | C32 | semidirect |
| 9. C3×#11758608 | C32 | semidirect |
| 10. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 11. C3×C32⋊(C37⋊C3) | C32 | semidirect |
| 14. #15688514 | C32 | semidirect |
| 15. #15688514 | C32 | semidirect |
| 17. C3×3−1+2×C37 | C32 | semidirect |
| 49. 3−1+4 | C37⋊C3 | semidirect |
| 64. C3×3−1+2 | C3×C37⋊C3 | semidirect |
| 72. C37 | #10624930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582680 | 3 |
| C37⋊H(5,𝔽3) | 3 |
| C3×H(3,𝔽3)×C37⋊C3 | 3 |
| #22582639 | 3 |
| C3×#15688514 | 3 |
| C37×3−1+4 | 3 |
| #10624930 | 37 |