Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. C2×C4×Dic218 | C2 | semidirect |
| 3. #20295362 | C2 | semidirect |
| 5. #20295334 | C2 | semidirect |
| 6. #20295249 | C2 | semidirect |
| 7. #20295184 | C2 | semidirect |
| 9. #20295134 | C2 | semidirect |
| 10. #20295128 | C2 | semidirect |
| 11. #432×C109 | C2 | semidirect |
| 132. C109 | #3117 | semidirect |
| 143. #432 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295560 | 2 |
| C2×C4×Dic218 | 2 |
| #20295362 | 2 |
| #20295345 | 2 |
| #20295334 | 2 |
| #20295249 | 2 |
| #20295184 | 2 |
| #20295167 | 2 |
| #20295134 | 2 |
| #20295128 | 2 |
| #432×C109 | 2 |
| #3117 | 109 |