Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
1082 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 280 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×#15688532 | C3 | semidirect |
| 2. C32×#11758608 | C3 | semidirect |
| 3. #22582565 | C3 | semidirect |
| 4. #22582561 | C3 | semidirect |
| 5. #22582560 | C3 | semidirect |
| 6. #22582557 | C3 | semidirect |
| 8. #22582539 | C3 | semidirect |
| 9. C3×C32⋊#66524 | C3 | semidirect |
| 10. C37×#6891 | C3 | semidirect |
| 16. C3×#11758605 | C32 | semidirect |
| 17. C3×#11758606 | C32 | semidirect |
| 23. C3×C9×C37⋊C3 | C32 | semidirect |
| 28. #15688502 | C32 | semidirect |
| 29. #15688502 | C32 | semidirect |
| 30. #15688502 | C32 | semidirect |
| 49. #11758608 | H(3,𝔽3) | semidirect |
| 71. C32×C37 | #737 | semidirect |
| 88. #6891 | C37⋊C3 | semidirect |
| 123. C37 | #10624896 | semidirect |
| 162. C32 | #15688532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688532 | 3 |
| C32×#11758608 | 3 |
| #22582565 | 3 |
| #22582561 | 3 |
| #22582560 | 3 |
| #22582557 | 3 |
| #22582550 | 3 |
| #22582539 | 3 |
| C3×C32⋊#66524 | 3 |
| C37×#6891 | 3 |
| #10624896 | 37 |