Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#16813644 | C2 | semidirect |
| 2. #20299109 | C2 | semidirect |
| 3. #20298856 | C2 | semidirect |
| 4. #20298851 | C2 | semidirect |
| 5. #20298844 | C2 | semidirect |
| 6. #20298636 | C2 | semidirect |
| 7. #20298595 | C2 | semidirect |
| 8. C22×M16×C113 | C2 | semidirect |
| 11. C2×Dic452 | C22 | semidirect |
| 12. C2×#14268636 | C22 | semidirect |
| 13. C2×D904 | C22 | semidirect |
| 20. #16813556 | C22 | semidirect |
| 21. #16813554 | C22 | semidirect |
| 22. #16813547 | C22 | semidirect |
| 23. #16813544 | C22 | semidirect |
| 56. C2×C8×C113 | D4 | semidirect |
| 106. C113 | #3054 | semidirect |
| 108. C22×M16 | D113 | semidirect |
| 156. C2×C8 | C22⋊D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813644 | 2 |
| #20299109 | 2 |
| #20298856 | 2 |
| #20298851 | 2 |
| #20298844 | 2 |
| #20298636 | 2 |
| #20298595 | 2 |
| C22×M16×C113 | 2 |
| #3054 | 113 |