Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
492 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 166 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×#16813709 | C2 | semidirect |
| 2. #20299633 | C2 | semidirect |
| 3. #20299629 | C2 | semidirect |
| 4. D4×#11744753 | C2 | semidirect |
| 5. #20299599 | C2 | semidirect |
| 6. #20299572 | C2 | semidirect |
| 7. C4×#14268657 | C2 | semidirect |
| 32. #14268657 | D4 | semidirect |
| 92. C4×C113 | #131 | semidirect |
| 104. C113 | #2935 | semidirect |
| 201. C4 | #16813709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813709 | 2 |
| #20299633 | 2 |
| #20299629 | 2 |
| D4×#11744753 | 2 |
| #20299599 | 2 |
| #20299572 | 2 |
| C4×#14268657 | 2 |
| #20299146 | 2 |
| #2935 | 113 |