Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#16812730 | C2 | semidirect |
| 2. C2×#16812729 | C2 | semidirect |
| 4. C22×#13182019 | C2 | semidirect |
| 5. #20295602 | C2 | semidirect |
| 6. #20295421 | C2 | semidirect |
| 7. #20295418 | C2 | semidirect |
| 8. #20295408 | C2 | semidirect |
| 9. #20295405 | C2 | semidirect |
| 10. #20294982 | C2 | semidirect |
| 11. #536×C109 | C2 | semidirect |
| 144. C109 | #3156 | semidirect |
| 150. #536 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812730 | 2 |
| C2×#16812729 | 2 |
| C2×#16812719 | 2 |
| C22×#13182019 | 2 |
| #20295602 | 2 |
| #20295421 | 2 |
| #20295418 | 2 |
| #20295408 | 2 |
| #20295405 | 2 |
| #20294982 | 2 |
| #536×C109 | 2 |
| #3156 | 109 |