Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 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 |
|---|---|---|
| 2. #20298948 | C2 | semidirect |
| 3. #20298926 | C2 | semidirect |
| 4. #20298883 | C2 | semidirect |
| 5. #20298829 | C2 | semidirect |
| 6. #20298800 | C2 | semidirect |
| 7. #20298737 | C2 | semidirect |
| 8. C4×#14268634 | C2 | semidirect |
| 9. D4×#11744751 | C2 | semidirect |
| 10. C2×#16813546 | C2 | semidirect |
| 11. D4×Q8×C113 | C2 | semidirect |
| 83. Q8×C113 | #41 | semidirect |
| 84. D4×C113 | SD16 | semidirect |
| 129. C113 | #3298 | semidirect |
| 130. D4×Q8 | D113 | semidirect |
| 213. Q8 | #14268646 | semidirect |
| 217. D4 | #14268634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299252 | 2 |
| #20298948 | 2 |
| #20298926 | 2 |
| #20298883 | 2 |
| #20298829 | 2 |
| #20298800 | 2 |
| #20298737 | 2 |
| C4×#14268634 | 2 |
| D4×#11744751 | 2 |
| C2×#16813546 | 2 |
| D4×Q8×C113 | 2 |
| #3298 | 113 |