Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 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 |
|---|---|---|
| 1. C2×#16813641 | C2 | semidirect |
| 2. #20299268 | C2 | semidirect |
| 3. #20298831 | C2 | semidirect |
| 4. #20298795 | C2 | semidirect |
| 5. #20298740 | C2 | semidirect |
| 6. C4×Dic452 | C2 | semidirect |
| 7. C8×D452 | C2 | semidirect |
| 8. #493×C113 | C2 | semidirect |
| 37. Dic452 | D4 | semidirect |
| 86. C4×C113 | #135 | semidirect |
| 98. C113 | #3287 | semidirect |
| 101. #493 | D113 | semidirect |
| 187. C4 | #16813641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813641 | 2 |
| #20299268 | 2 |
| #20298831 | 2 |
| #20298795 | 2 |
| #20298740 | 2 |
| C4×Dic452 | 2 |
| C8×D452 | 2 |
| #493×C113 | 2 |
| #3287 | 113 |