Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16813643 | C2 | semidirect |
| 2. C2×#16813641 | C2 | semidirect |
| 3. #20299147 | C2 | semidirect |
| 4. #20299146 | C2 | semidirect |
| 5. #20298993 | C2 | semidirect |
| 6. #20298992 | C2 | semidirect |
| 7. #20298989 | C2 | semidirect |
| 8. #20298986 | C2 | semidirect |
| 9. #20298985 | C2 | semidirect |
| 10. #97×D113 | C2 | semidirect |
| 11. #496×C113 | C2 | semidirect |
| 64. C8×D113 | D4 | semidirect |
| 134. C113 | #3150 | semidirect |
| 144. #496 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813643 | 2 |
| C2×#16813641 | 2 |
| #20299147 | 2 |
| #20299146 | 2 |
| #20298993 | 2 |
| #20298992 | 2 |
| #20298989 | 2 |
| #20298986 | 2 |
| #20298985 | 2 |
| #97×D113 | 2 |
| #496×C113 | 2 |
| #3150 | 113 |