Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
730 conjugacy classes of subgroups; only the 295 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 295 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 |
|---|---|---|
| 2. #22582575 | C3 | semidirect |
| 3. #22582573 | C3 | semidirect |
| 4. #22582573 | C3 | semidirect |
| 5. #22582572 | C3 | semidirect |
| 8. C3×#15688504 | C3 | semidirect |
| 55. #66524 | #737 | semidirect |
| 87. C37 | #10624900 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#15688530 | 3 |
| #22582575 | 3 |
| #22582573 | 3 |
| #22582572 | 3 |
| H(3,𝔽3)×#66524 | 3 |
| C3×#15688504 | 3 |
| C9×H(3,𝔽3)×C37 | 3 |
| #10624900 | 37 |