Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20299309 | C2 | semidirect |
| 3. #20298915 | C2 | semidirect |
| 4. #20298885 | C2 | semidirect |
| 5. #20298826 | C2 | semidirect |
| 6. #20298795 | C2 | semidirect |
| 7. #20298750 | C2 | semidirect |
| 8. C4×#14268636 | C2 | semidirect |
| 9. C8×D452 | C2 | semidirect |
| 10. #102×D113 | C2 | semidirect |
| 11. #486×C113 | C2 | semidirect |
| 15. C2×#14268635 | C22 | semidirect |
| 16. C2×C8×D113 | C22 | semidirect |
| 18. #16813602 | C22 | semidirect |
| 23. C4×Dic226 | C22 | semidirect |
| 27. C4⋊C4×D113 | C22 | semidirect |
| 28. #16813554 | C22 | semidirect |
| 29. #16813553 | C22 | semidirect |
| 30. C4⋊#11744751 | C22 | semidirect |
| 31. #16813547 | C22 | semidirect |
| 33. #16813543 | C22 | semidirect |
| 35. #16813534 | C22 | semidirect |
| 36. C4⋊Q8×C113 | C22 | semidirect |
| 38. #102×C113 | C22 | semidirect |
| 39. #102×C113 | C22 | semidirect |
| 40. C4×C8×C113 | C22 | semidirect |
| 99. D452 | SD16 | semidirect |
| 137. C113 | #3295 | semidirect |
| 140. #486 | D113 | semidirect |
| 154. C4⋊Q8 | C2×D113 | semidirect |
| 174. #102 | C2×D113 | semidirect |
| 175. #102 | C2×D113 | semidirect |
| 177. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299309 | 2 |
| #20299233 | 2 |
| #20298915 | 2 |
| #20298885 | 2 |
| #20298826 | 2 |
| #20298795 | 2 |
| #20298750 | 2 |
| C4×#14268636 | 2 |
| C8×D452 | 2 |
| #102×D113 | 2 |
| #486×C113 | 2 |
| #3295 | 113 |