Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 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. C22×#14268637 | C2 | semidirect |
| 3. C2×Q8×Dic113 | C2 | semidirect |
| 4. #20298818 | C2 | direct (N × H) |
| 5. C2×#16813551 | C2 | semidirect |
| 6. C2×#16813547 | C2 | semidirect |
| 11. C2×#14268637 | C22 | semidirect |
| 16. Q8×Dic113 | C22 | semidirect |
| 23. #16813551 | C22 | semidirect |
| 24. #16813547 | C22 | semidirect |
| 111. C2×C113 | #464 | semidirect |
| 116. C113 | C2×#464 | semidirect |
| 227. C2 | #20298818 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14268637 | 2 |
| C2×#16813609 | 2 |
| C2×Q8×Dic113 | 2 |
| #20298818 | 2 |
| C2×#16813551 | 2 |
| C2×#16813547 | 2 |
| C2×#16813543 | 2 |
| C22×SD16×C113 | 2 |
| C2×#464 | 113 |