Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1166 conjugacy classes of subgroups; only the 310 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 310 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. C3×#15688531 | C3 | semidirect |
| 2. #22582564 | C3 | semidirect |
| 3. #22582559 | C3 | semidirect |
| 4. #22582558 | C3 | semidirect |
| 5. #22582554 | C3 | semidirect |
| 7. C9×C32⋊(C37⋊C3) | C3 | semidirect |
| 8. C33×C9×C37 | C3 | semidirect |
| 11. C3×#11758605 | C32 | semidirect |
| 12. C3×#11758606 | C32 | semidirect |
| 15. C3×C9×C37⋊C3 | C32 | semidirect |
| 17. #15688502 | C32 | semidirect |
| 34. C3×C9×C37 | H(3,𝔽3) | semidirect |
| 52. C32×C37 | #737 | semidirect |
| 62. C33×C9 | C37⋊C3 | semidirect |
| 90. C37 | #10624869 | semidirect |
| 107. C3×C9 | C32⋊(C37⋊C3) | semidirect |
| 119. C32 | #15688531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688531 | 3 |
| #22582564 | 3 |
| #22582559 | 3 |
| #22582558 | 3 |
| #22582554 | 3 |
| #22582550 | 3 |
| C9×C32⋊(C37⋊C3) | 3 |
| C33×C9×C37 | 3 |
| #10624869 | 37 |