Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812732 | C2 | semidirect |
| 3. #20295602 | C2 | semidirect |
| 4. #20295506 | C2 | semidirect |
| 5. #20295249 | C2 | semidirect |
| 6. #20295242 | C2 | semidirect |
| 7. #20295237 | C2 | semidirect |
| 8. #20295232 | C2 | semidirect |
| 9. #20295028 | C2 | semidirect |
| 10. C2×#16812624 | C2 | semidirect |
| 11. #424×C109 | C2 | semidirect |
| 147. C109 | #3046 | semidirect |
| 156. #424 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812732 | 2 |
| C2×#16812721 | 2 |
| #20295602 | 2 |
| #20295506 | 2 |
| #20295249 | 2 |
| #20295242 | 2 |
| #20295237 | 2 |
| #20295232 | 2 |
| #20295028 | 2 |
| C2×#16812624 | 2 |
| #424×C109 | 2 |
| #3046 | 109 |