Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16813652 | C2 | semidirect |
| 2. C2×#16813609 | C2 | semidirect |
| 3. #41×Dic113 | C2 | semidirect |
| 4. #20298818 | C2 | semidirect |
| 5. #20298811 | C2 | semidirect |
| 6. #20298621 | C2 | semidirect |
| 7. #20298608 | C2 | semidirect |
| 8. #20298603 | C2 | semidirect |
| 12. C2×#14268637 | C22 | semidirect |
| 13. C2×#14268635 | C22 | semidirect |
| 18. Q8×Dic113 | C22 | semidirect |
| 20. D4×Dic113 | C22 | semidirect |
| 26. #16813551 | C22 | semidirect |
| 27. #16813547 | C22 | semidirect |
| 126. C113 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813652 | 2 |
| C2×#16813609 | 2 |
| #41×Dic113 | 2 |
| #20298818 | 2 |
| #20298811 | 2 |
| #20298621 | 2 |
| #20298608 | 2 |
| #20298603 | 2 |
| C2×AGL(1,ℤ/8)×C113 | 2 |
| #3040 | 113 |