Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
456 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 2. #20299638 | C2 | semidirect |
| 3. Q16×#90673 | C2 | semidirect |
| 20. C2×Dic452 | C4 | semidirect |
| 21. C2×#14268637 | C4 | semidirect |
| 22. Q16×D113 | C4 | semidirect |
| 23. Q16×D113 | C4 | semidirect |
| 27. C2×Q16×C113 | C4 | semidirect |
| 101. C113 | #2950 | semidirect |
| 116. C2×Q16 | #90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299666 | 2 |
| #20299638 | 2 |
| Q16×#90673 | 2 |
| #20299608 | 2 |
| #20299591 | 2 |
| #20299561 | 2 |
| C2×Q16×D113 | 2 |
| #2950 | 113 |