Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 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. C22×#14268637 | C2 | semidirect |
| 3. #20298754 | C2 | direct (N × H) |
| 4. C2×#16813546 | C2 | semidirect |
| 9. C2×#14268637 | C22 | semidirect |
| 16. #16813546 | C22 | semidirect |
| 56. C23×C113 | Q16 | semidirect |
| 85. C22×C113 | C2×Q16 | semidirect |
| 95. C2×C113 | #451 | semidirect |
| 100. C113 | C2×#451 | semidirect |
| 156. C23 | #14268637 | semidirect |
| 185. C22 | C2×#14268637 | semidirect |
| 195. C2 | #20298754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268637 | 2 |
| C2×#16813601 | 2 |
| #20298754 | 2 |
| C2×#16813546 | 2 |
| C2×C22⋊#11744751 | 2 |
| C23×Q8×C113 | 2 |
| C2×#451 | 113 |