Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20299308 | C2 | semidirect |
| 3. #20298945 | C2 | semidirect |
| 4. #20298913 | C2 | semidirect |
| 5. #20298893 | C2 | semidirect |
| 6. #20298847 | C2 | semidirect |
| 7. #20298798 | C2 | semidirect |
| 8. #20298759 | C2 | semidirect |
| 9. #20298677 | C2 | semidirect |
| 10. #20298598 | C2 | semidirect |
| 11. C4×Q16×C113 | C2 | semidirect |
| 129. C113 | #3333 | semidirect |
| 138. C4×Q16 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299308 | 2 |
| #20299270 | 2 |
| #20298945 | 2 |
| #20298913 | 2 |
| #20298893 | 2 |
| #20298847 | 2 |
| #20298798 | 2 |
| #20298759 | 2 |
| #20298677 | 2 |
| #20298598 | 2 |
| C4×Q16×C113 | 2 |
| #3333 | 113 |