Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16813644 | C2 | semidirect |
| 2. C2×#16813642 | C2 | semidirect |
| 3. #20299144 | C2 | semidirect |
| 4. #20298991 | C2 | semidirect |
| 5. #20298989 | C2 | semidirect |
| 6. #20298986 | C2 | semidirect |
| 7. #20298984 | C2 | semidirect |
| 8. C2×#16813532 | C2 | semidirect |
| 9. C2×#135×C113 | C2 | semidirect |
| 51. C2×#11744751 | D4 | semidirect |
| 68. C2×C8×C113 | D4 | semidirect |
| 117. C113 | #3150 | semidirect |
| 120. C2×#135 | D113 | semidirect |
| 180. C2×C8 | C22⋊D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813644 | 2 |
| C2×#16813642 | 2 |
| #20299144 | 2 |
| #20298991 | 2 |
| #20298989 | 2 |
| #20298986 | 2 |
| #20298984 | 2 |
| C2×#16813532 | 2 |
| C2×#135×C113 | 2 |
| #3150 | 113 |