Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
412 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 78 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×#16813701 | C2 | semidirect |
| 2. C2×#16813684 | C2 | semidirect |
| 3. #20299566 | C2 | semidirect |
| 4. #20299471 | C2 | semidirect |
| 17. #16813597 | C4 | semidirect |
| 18. #16813596 | C4 | semidirect |
| 21. #16813593 | C4 | semidirect |
| 24. #121×C113 | C4 | semidirect |
| 30. C4⋊#90673 | D4 | semidirect |
| 138. C113 | #1875 | semidirect |
| 153. #121 | #90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813701 | 2 |
| C2×#16813684 | 2 |
| #20299566 | 2 |
| #20299471 | 2 |
| #121×D113 | 2 |
| #1875 | 113 |