Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 1. #20299148 | C2 | semidirect |
| 2. C2×C4×D452 | C2 | semidirect |
| 3. #20298912 | C2 | semidirect |
| 4. #20298879 | C2 | semidirect |
| 5. #20298794 | C2 | semidirect |
| 6. #20298734 | C2 | semidirect |
| 7. C4×D904 | C2 | semidirect |
| 8. #431×C113 | C2 | semidirect |
| 13. #16813622 | C22 | semidirect |
| 14. #16813619 | C22 | semidirect |
| 23. C4×D452 | C22 | semidirect |
| 26. #16813556 | C22 | semidirect |
| 28. #16813544 | C22 | semidirect |
| 30. C4⋊C8×C113 | C22 | semidirect |
| 32. C4×C8×C113 | C22 | semidirect |
| 73. C2×C4×C113 | D8 | semidirect |
| 89. D452 | #41 | semidirect |
| 121. C113 | #3100 | semidirect |
| 129. #431 | D113 | semidirect |
| 149. C4⋊C8 | C2×D113 | semidirect |
| 153. C4×C8 | C2×D113 | semidirect |
| 208. C2×C4 | D904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299148 | 2 |
| C2×C4×D452 | 2 |
| #20298912 | 2 |
| #20298879 | 2 |
| #20298794 | 2 |
| #20298734 | 2 |
| C4×D904 | 2 |
| #431×C113 | 2 |
| #3100 | 113 |