Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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×D8×D113 | C2 | semidirect |
| 2. #20299233 | C2 | semidirect |
| 3. #20298831 | C2 | semidirect |
| 4. #20298790 | C2 | semidirect |
| 5. #20298730 | C2 | semidirect |
| 6. C4×D904 | C2 | semidirect |
| 7. C8×D452 | C2 | semidirect |
| 8. #493×C113 | C2 | semidirect |
| 10. C2×D4×D113 | C22 | semidirect |
| 12. C2×#14268632 | C22 | semidirect |
| 14. C2×C8×D113 | C22 | semidirect |
| 16. #16813593 | C22 | semidirect |
| 19. C4×D452 | C22 | semidirect |
| 20. #16813556 | C22 | semidirect |
| 21. C4⋊#11744751 | C22 | semidirect |
| 22. #16813544 | C22 | semidirect |
| 23. #16813543 | C22 | semidirect |
| 24. #16813534 | C22 | semidirect |
| 25. C2×D8×C113 | C22 | semidirect |
| 26. C2×D8×C113 | C22 | semidirect |
| 27. #127×C113 | C22 | semidirect |
| 28. C4×C8×C113 | C22 | semidirect |
| 39. D904 | D4 | semidirect |
| 74. D452 | D8 | semidirect |
| 75. D452 | C2×D4 | semidirect |
| 80. C8×C113 | C2×D4 | semidirect |
| 92. C2×D113 | C2×D8 | semidirect |
| 94. C4×C113 | C2×D8 | semidirect |
| 106. C113 | D4×D8 | semidirect |
| 109. #493 | D113 | semidirect |
| 120. C2×D8 | C2×D113 | semidirect |
| 121. C2×D8 | C2×D113 | semidirect |
| 123. #127 | C2×D113 | semidirect |
| 134. C4×C8 | C2×D113 | semidirect |
| 187. C8 | D4×D113 | semidirect |
| 202. C4 | D8×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D113 | 2 |
| #20299233 | 2 |
| #20298831 | 2 |
| #20298790 | 2 |
| #20298730 | 2 |
| C4×D904 | 2 |
| C8×D452 | 2 |
| #493×C113 | 2 |
| D4×D8 | 113 |