Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20299146 | C2 | semidirect |
| 3. C4×#14268648 | C2 | semidirect |
| 4. #20298818 | C2 | semidirect |
| 5. #20298812 | C2 | semidirect |
| 6. #20298808 | C2 | semidirect |
| 7. #20298804 | C2 | semidirect |
| 8. #20298790 | C2 | semidirect |
| 9. C4⋊C8×D113 | C2 | semidirect |
| 10. #20298591 | C2 | semidirect |
| 11. #460×C113 | C2 | semidirect |
| 45. #14268648 | D4 | semidirect |
| 136. C4×C113 | #135 | semidirect |
| 151. C113 | #3035 | semidirect |
| 159. #460 | D113 | semidirect |
| 292. C4 | #16813643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813643 | 2 |
| #20299146 | 2 |
| C4×#14268648 | 2 |
| #20298818 | 2 |
| #20298812 | 2 |
| #20298808 | 2 |
| #20298804 | 2 |
| #20298790 | 2 |
| C4⋊C8×D113 | 2 |
| #20298591 | 2 |
| #460×C113 | 2 |
| #3035 | 113 |