Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22582614 | C3 | semidirect |
| 3. #22582613 | C3 | semidirect |
| 4. C3×#15688509 | C3 | semidirect |
| 5. #22582486 | C3 | semidirect |
| 6. #22582485 | C3 | semidirect |
| 7. #22582484 | C3 | semidirect |
| 8. #22582473 | C3 | semidirect |
| 9. C37×#6872 | C3 | semidirect |
| 75. #6872 | C37⋊C3 | semidirect |
| 104. C37 | #10624725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582630 | 3 |
| #22582614 | 3 |
| #22582613 | 3 |
| C3×#15688509 | 3 |
| #22582486 | 3 |
| #22582485 | 3 |
| #22582484 | 3 |
| #22582473 | 3 |
| C37×#6872 | 3 |
| #10624725 | 37 |