Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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×#16813621 | C2 | semidirect |
| 3. #20298959 | C2 | semidirect |
| 4. #20298956 | C2 | semidirect |
| 5. #20298947 | C2 | semidirect |
| 6. #20298943 | C2 | semidirect |
| 7. #20298600 | C2 | semidirect |
| 8. #20298599 | C2 | semidirect |
| 9. #20298597 | C2 | semidirect |
| 10. M16×Dic113 | C2 | semidirect |
| 11. #417×C113 | C2 | semidirect |
| 150. C113 | #3141 | semidirect |
| 160. #417 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299144 | 2 |
| C2×#16813621 | 2 |
| #20298959 | 2 |
| #20298956 | 2 |
| #20298947 | 2 |
| #20298943 | 2 |
| #20298600 | 2 |
| #20298599 | 2 |
| #20298597 | 2 |
| M16×Dic113 | 2 |
| #417×C113 | 2 |
| #3141 | 113 |