Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16812729 | C2 | semidirect |
| 2. C2×#16812705 | C2 | semidirect |
| 4. #20295602 | C2 | semidirect |
| 5. #20295283 | C2 | semidirect |
| 6. #20295271 | C2 | semidirect |
| 7. #20295266 | C2 | semidirect |
| 8. #20295254 | C2 | semidirect |
| 9. #20295069 | C2 | semidirect |
| 10. C2×#16812624 | C2 | semidirect |
| 11. #416×C109 | C2 | semidirect |
| 58. #13182013 | D4 | semidirect |
| 144. C109 | #3063 | semidirect |
| 154. #416 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812729 | 2 |
| C2×#16812705 | 2 |
| #20295604 | 2 |
| #20295602 | 2 |
| #20295283 | 2 |
| #20295271 | 2 |
| #20295266 | 2 |
| #20295254 | 2 |
| #20295069 | 2 |
| C2×#16812624 | 2 |
| #416×C109 | 2 |
| #3063 | 109 |