Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 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. #20299321 | C2 | semidirect |
| 3. #20298945 | C2 | semidirect |
| 4. #20298925 | C2 | semidirect |
| 5. #20298883 | C2 | semidirect |
| 6. #20298830 | C2 | semidirect |
| 7. #20298798 | C2 | semidirect |
| 8. #20298759 | C2 | semidirect |
| 9. C8×D452 | C2 | semidirect |
| 10. #20298593 | C2 | semidirect |
| 11. C4×Q16×C113 | C2 | semidirect |
| 128. C113 | #3304 | semidirect |
| 137. C4×Q16 | D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299321 | 2 |
| #20299270 | 2 |
| #20298945 | 2 |
| #20298925 | 2 |
| #20298883 | 2 |
| #20298830 | 2 |
| #20298798 | 2 |
| #20298759 | 2 |
| C8×D452 | 2 |
| #20298593 | 2 |
| C4×Q16×C113 | 2 |
| #3304 | 113 |