Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D452 | C2 | semidirect |
| 3. #20298949 | C2 | semidirect |
| 4. #20298930 | C2 | semidirect |
| 5. #20298883 | C2 | semidirect |
| 6. #20298826 | C2 | semidirect |
| 7. #20298803 | C2 | semidirect |
| 8. #20298735 | C2 | semidirect |
| 9. C8×D452 | C2 | semidirect |
| 10. #103×D113 | C2 | semidirect |
| 11. C4×SD16×C113 | C2 | semidirect |
| 80. Q8×C113 | #41 | semidirect |
| 94. D452 | SD16 | semidirect |
| 129. C113 | #3298 | semidirect |
| 138. C4×SD16 | D113 | semidirect |
| 213. Q8 | #14268647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D452 | 2 |
| #20299253 | 2 |
| #20298949 | 2 |
| #20298930 | 2 |
| #20298883 | 2 |
| #20298826 | 2 |
| #20298803 | 2 |
| #20298735 | 2 |
| C8×D452 | 2 |
| #103×D113 | 2 |
| C4×SD16×C113 | 2 |
| #3298 | 113 |