Finite Group DatabasebetaFinite Group DatabasebetaOrder 26973.
198 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 52 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. #22582572 | C3 | semidirect |
| 2. #22582564 | C3 | semidirect |
| 3. #22582559 | C3 | semidirect |
| 4. #22582455 | C3 | semidirect |
| 5. #22582454 | C3 | semidirect |
| 6. #22582453 | C3 | semidirect |
| 7. #22582450 | C3 | semidirect |
| 8. #22582449 | C3 | semidirect |
| 9. #22582446 | C3 | semidirect |
| 10. #22582444 | C3 | semidirect |
| 11. #22582444 | C3 | semidirect |
| 13. C37×#6894 | C3 | semidirect |
| 91. #6894 | C37⋊C3 | semidirect |
| 135. C37 | #10624677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582572 | 3 |
| #22582564 | 3 |
| #22582559 | 3 |
| #22582455 | 3 |
| #22582454 | 3 |
| #22582453 | 3 |
| #22582450 | 3 |
| #22582449 | 3 |
| #22582446 | 3 |
| #22582444 | 3 |
| #22582443 | 3 |
| C37×#6894 | 3 |
| #10624677 | 37 |