Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
756 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 198 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. #20296104 | C2 | semidirect |
| 2. #20296013 | C2 | semidirect |
| 3. #20296012 | C2 | semidirect |
| 4. D109⋊#100 | C2 | semidirect |
| 5. C2×#16812759 | C2 | semidirect |
| 8. D109⋊M16 | C22 | semidirect |
| 9. C2×#13182038 | C22 | semidirect |
| 10. #16812760 | C22 | semidirect |
| 11. #16812759 | C22 | semidirect |
| 12. #16812759 | C22 | semidirect |
| 132. C109 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296104 | 2 |
| #20296013 | 2 |
| #20296012 | 2 |
| D109⋊#100 | 2 |
| C2×#16812759 | 2 |
| C2×#16812744 | 2 |
| #2888 | 109 |