Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. C22×#14268635 | C2 | semidirect |
| 2. #20299169 | C2 | semidirect |
| 3. #20299073 | C2 | semidirect |
| 4. #20298811 | C2 | semidirect |
| 5. #20298801 | C2 | semidirect |
| 6. #20298626 | C2 | semidirect |
| 7. #20298608 | C2 | semidirect |
| 8. #20298594 | C2 | semidirect |
| 14. #16813620 | C22 | semidirect |
| 15. #16813609 | C22 | semidirect |
| 23. #16813551 | C22 | semidirect |
| 24. #16813547 | C22 | semidirect |
| 25. #16813546 | C22 | semidirect |
| 26. #16813543 | C22 | semidirect |
| 117. C113 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268635 | 2 |
| #20299169 | 2 |
| #20299073 | 2 |
| #20298811 | 2 |
| #20298801 | 2 |
| #20298626 | 2 |
| #20298608 | 2 |
| #20298594 | 2 |
| C2×AGL(1,ℤ/8)×C113 | 2 |
| #3042 | 113 |