Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20295824 | C2 | semidirect |
| 2. C2×#16812727 | C2 | semidirect |
| 3. C2×#16812724 | C2 | semidirect |
| 4. #20295296 | C2 | semidirect |
| 5. #20295289 | C2 | semidirect |
| 6. #20295075 | C2 | semidirect |
| 7. #20295008 | C2 | semidirect |
| 8. C2×#16812615 | C2 | semidirect |
| 9. #568×C109 | C2 | semidirect |
| 13. #16812729 | C22 | semidirect |
| 19. #16812724 | C22 | semidirect |
| 21. C2×#13182018 | C22 | semidirect |
| 23. C2×D872 | C22 | semidirect |
| 27. #16812635 | C22 | semidirect |
| 28. #16812617 | C22 | semidirect |
| 29. #16812615 | C22 | semidirect |
| 30. #16812615 | C22 | semidirect |
| 33. #131×C109 | C22 | semidirect |
| 148. C109 | #3068 | semidirect |
| 152. #568 | D109 | semidirect |
| 175. #131 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295824 | 2 |
| C2×#16812727 | 2 |
| C2×#16812724 | 2 |
| #20295296 | 2 |
| #20295289 | 2 |
| #20295075 | 2 |
| #20295008 | 2 |
| C2×#16812615 | 2 |
| #568×C109 | 2 |
| #3068 | 109 |