Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16812718 | C2 | semidirect |
| 2. C22×Dic436 | C2 | semidirect |
| 3. #20295682 | C2 | semidirect |
| 4. #20295409 | C2 | semidirect |
| 5. #20295268 | C2 | semidirect |
| 6. #20295247 | C2 | semidirect |
| 7. #20295189 | C2 | semidirect |
| 8. #20295164 | C2 | semidirect |
| 9. #20295120 | C2 | semidirect |
| 10. C8×C22⋊D109 | C2 | semidirect |
| 11. #466×C109 | C2 | semidirect |
| 55. Dic436 | D4 | semidirect |
| 116. C22×C109 | #135 | semidirect |
| 137. C109 | #3285 | semidirect |
| 143. #466 | D109 | semidirect |
| 256. C22 | #16812718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812718 | 2 |
| C22×Dic436 | 2 |
| #20295682 | 2 |
| #20295409 | 2 |
| #20295268 | 2 |
| #20295247 | 2 |
| #20295189 | 2 |
| #20295164 | 2 |
| #20295120 | 2 |
| C8×C22⋊D109 | 2 |
| #466×C109 | 2 |
| #3285 | 109 |