Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20299333 | C2 | semidirect |
| 2. D4×Dic226 | C2 | semidirect |
| 3. #20298959 | C2 | semidirect |
| 4. #20298945 | C2 | semidirect |
| 5. #20298887 | C2 | semidirect |
| 6. #20298883 | C2 | semidirect |
| 7. #20298815 | C2 | semidirect |
| 9. #20298728 | C2 | semidirect |
| 10. #20298707 | C2 | semidirect |
| 11. C4×SD16×C113 | C2 | semidirect |
| 125. C113 | #3373 | semidirect |
| 136. C4×SD16 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299333 | 2 |
| D4×Dic226 | 2 |
| #20298959 | 2 |
| #20298945 | 2 |
| #20298887 | 2 |
| #20298883 | 2 |
| #20298815 | 2 |
| #20298793 | 2 |
| #20298728 | 2 |
| #20298707 | 2 |
| C4×SD16×C113 | 2 |
| #3373 | 113 |