Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. C2×#16813557 | C2 | semidirect |
| 3. #20298634 | C2 | semidirect |
| 6. #20298370 | C2 | semidirect |
| 7. #344×C113 | C2 | semidirect |
| 11. #16813630 | C4 | semidirect |
| 12. #16813630 | C4 | semidirect |
| 106. C113 | #1814 | semidirect |
| 113. #344 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813630 | 2 |
| C2×#16813557 | 2 |
| #20298634 | 2 |
| #20298616 | 2 |
| #20298614 | 2 |
| #20298370 | 2 |
| #344×C113 | 2 |
| #1814 | 113 |