Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
500 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 229 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×#16813629 | C2 | semidirect |
| 2. #20298676 | C2 | semidirect |
| 3. D4×#11744751 | C2 | semidirect |
| 4. #20298622 | C2 | semidirect |
| 5. #20298565 | C2 | semidirect |
| 6. C2×C4×#11744751 | C2 | semidirect |
| 29. C2×#11744751 | D4 | semidirect |
| 76. C4×C113 | #131 | semidirect |
| 84. C113 | #2931 | semidirect |
| 160. C4 | #16813629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813629 | 2 |
| #20298676 | 2 |
| D4×#11744751 | 2 |
| #20298622 | 2 |
| #20298565 | 2 |
| C2×C4×#11744751 | 2 |
| #532×C113 | 2 |
| #2931 | 113 |