Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20299313 | C2 | semidirect |
| 2. D4×D452 | C2 | semidirect |
| 3. #20298945 | C2 | semidirect |
| 4. #20298925 | C2 | semidirect |
| 5. #20298888 | C2 | semidirect |
| 6. #20298850 | C2 | semidirect |
| 7. #20298793 | C2 | semidirect |
| 8. #20298730 | C2 | semidirect |
| 9. #20298677 | C2 | semidirect |
| 10. #20298601 | C2 | semidirect |
| 11. C4×D8×C113 | C2 | semidirect |
| 14. C2×#14268632 | C22 | semidirect |
| 15. C2×#14268630 | C22 | semidirect |
| 16. #16813622 | C22 | semidirect |
| 22. #16813593 | C22 | semidirect |
| 26. #16813580 | C22 | semidirect |
| 27. #16813553 | C22 | semidirect |
| 28. C4⋊#11744751 | C22 | semidirect |
| 29. #16813544 | C22 | semidirect |
| 30. #16813544 | C22 | semidirect |
| 32. #16813542 | C22 | semidirect |
| 33. #16813534 | C22 | semidirect |
| 36. C4×D4×C113 | C22 | semidirect |
| 37. #107×C113 | C22 | semidirect |
| 39. #102×C113 | C22 | semidirect |
| 40. C4×C8×C113 | C22 | semidirect |
| 141. C113 | #3325 | semidirect |
| 150. C4×D8 | D113 | semidirect |
| 168. C4×D4 | C2×D113 | semidirect |
| 171. #107 | C2×D113 | semidirect |
| 179. #102 | C2×D113 | semidirect |
| 181. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299313 | 2 |
| D4×D452 | 2 |
| #20298945 | 2 |
| #20298925 | 2 |
| #20298888 | 2 |
| #20298850 | 2 |
| #20298793 | 2 |
| #20298730 | 2 |
| #20298677 | 2 |
| #20298601 | 2 |
| C4×D8×C113 | 2 |
| #3325 | 113 |