Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#16813642 | C2 | semidirect |
| 2. #20299148 | C2 | semidirect |
| 3. #20298980 | C2 | semidirect |
| 4. #20298977 | C2 | semidirect |
| 5. #20298974 | C2 | semidirect |
| 6. #20298972 | C2 | semidirect |
| 7. #20298970 | C2 | semidirect |
| 8. C2×C4×#11744751 | C2 | semidirect |
| 9. #532×C113 | C2 | semidirect |
| 42. C2×#11744751 | D4 | semidirect |
| 93. C4×C113 | #135 | semidirect |
| 102. C113 | #3147 | semidirect |
| 105. #532 | D113 | semidirect |
| 196. C4 | #16813642 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813642 | 2 |
| #20299148 | 2 |
| #20298980 | 2 |
| #20298977 | 2 |
| #20298974 | 2 |
| #20298972 | 2 |
| #20298970 | 2 |
| C2×C4×#11744751 | 2 |
| #532×C113 | 2 |
| #3147 | 113 |