Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#16812705 | C2 | semidirect |
| 3. #20295605 | C2 | semidirect |
| 4. #20295271 | C2 | semidirect |
| 5. #20295270 | C2 | semidirect |
| 6. #20295268 | C2 | semidirect |
| 7. #20295267 | C2 | semidirect |
| 8. #20295259 | C2 | semidirect |
| 9. #107×D109 | C2 | semidirect |
| 10. #20295024 | C2 | semidirect |
| 11. #466×C109 | C2 | semidirect |
| 64. C8×D109 | D4 | semidirect |
| 144. C109 | #3061 | semidirect |
| 153. #466 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812718 | 2 |
| C2×#16812705 | 2 |
| #20295605 | 2 |
| #20295271 | 2 |
| #20295270 | 2 |
| #20295268 | 2 |
| #20295267 | 2 |
| #20295259 | 2 |
| #107×D109 | 2 |
| #20295024 | 2 |
| #466×C109 | 2 |
| #3061 | 109 |