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×#16813652 | C2 | semidirect |
| 3. C2×#16813610 | C2 | semidirect |
| 4. #20298820 | C2 | semidirect |
| 5. #20298813 | C2 | semidirect |
| 6. #20298622 | C2 | semidirect |
| 7. #20298606 | C2 | semidirect |
| 8. #20298602 | C2 | semidirect |
| 9. C4×#41×C113 | C2 | semidirect |
| 14. C2×#14268637 | C22 | semidirect |
| 15. C2×#14268635 | C22 | semidirect |
| 24. C4⋊#11744751 | C22 | semidirect |
| 25. #16813545 | C22 | semidirect |
| 28. C4×Q8×C113 | C22 | semidirect |
| 30. C4×D4×C113 | C22 | semidirect |
| 126. C113 | #3040 | semidirect |
| 130. C4×#41 | D113 | semidirect |
| 150. C4×Q8 | C2×D113 | semidirect |
| 152. C4×D4 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813652 | 2 |
| C2×#16813647 | 2 |
| C2×#16813610 | 2 |
| #20298820 | 2 |
| #20298813 | 2 |
| #20298622 | 2 |
| #20298606 | 2 |
| #20298602 | 2 |
| C4×#41×C113 | 2 |
| #3040 | 113 |