Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20298994 | C2 | semidirect |
| 3. #20298926 | C2 | semidirect |
| 4. #20298916 | C2 | semidirect |
| 5. #20298885 | C2 | semidirect |
| 6. #20298883 | C2 | semidirect |
| 7. #20298829 | C2 | semidirect |
| 8. C4×#14268634 | C2 | semidirect |
| 9. D4×#11744751 | C2 | semidirect |
| 10. C2×#16813553 | C2 | semidirect |
| 11. #554×C113 | C2 | semidirect |
| 79. D4×C113 | SD16 | semidirect |
| 100. #11744751 | #41 | semidirect |
| 124. C113 | #3335 | semidirect |
| 125. #554 | D113 | semidirect |
| 207. D4 | #14268634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299252 | 2 |
| #20298994 | 2 |
| #20298926 | 2 |
| #20298916 | 2 |
| #20298885 | 2 |
| #20298883 | 2 |
| #20298829 | 2 |
| C4×#14268634 | 2 |
| D4×#11744751 | 2 |
| C2×#16813553 | 2 |
| #554×C113 | 2 |
| #3335 | 113 |