Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
1102 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 213 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×#16812682 | C2 | semidirect |
| 3. #20294905 | C2 | semidirect |
| 4. #20294899 | C2 | semidirect |
| 5. #20294889 | C2 | semidirect |
| 6. #20294882 | C2 | semidirect |
| 7. C24×C4×C109 | C2 | semidirect |
| 12. C2×#13182008 | C22 | semidirect |
| 17. C2×#13182006 | C22 | semidirect |
| 18. #16812606 | C22 | semidirect |
| 48. C22×C4×C109 | D4 | semidirect |
| 84. C22×C109 | #123 | semidirect |
| 102. C109 | #2849 | semidirect |
| 103. C24×C4 | D109 | semidirect |
| 144. C22×C4 | C22⋊D109 | semidirect |
| 189. C22 | #16812682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812682 | 2 |
| C2×#16812668 | 2 |
| #20294905 | 2 |
| #20294899 | 2 |
| #20294889 | 2 |
| #20294882 | 2 |
| C24×C4×C109 | 2 |
| #2849 | 109 |