Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20299153 | C2 | semidirect |
| 3. #20298971 | C2 | semidirect |
| 4. #20298970 | C2 | semidirect |
| 5. #20298946 | C2 | semidirect |
| 6. #20298797 | C2 | semidirect |
| 7. #20298750 | C2 | semidirect |
| 8. #20298649 | C2 | semidirect |
| 9. #486×C113 | C2 | semidirect |
| 13. C2×#14268636 | C22 | semidirect |
| 14. C2×#14268635 | C22 | semidirect |
| 15. #16813622 | C22 | semidirect |
| 24. #16813587 | C22 | semidirect |
| 27. #16813551 | C22 | semidirect |
| 28. #16813542 | C22 | semidirect |
| 30. C4×#11744751 | C22 | semidirect |
| 31. C4⋊Q8×C113 | C22 | semidirect |
| 33. #102×C113 | C22 | semidirect |
| 34. C4×C8×C113 | C22 | semidirect |
| 95. C4×D113 | SD16 | semidirect |
| 125. C113 | #3208 | semidirect |
| 131. #486 | D113 | semidirect |
| 141. C4⋊Q8 | C2×D113 | semidirect |
| 156. #102 | C2×D113 | semidirect |
| 159. C4×C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299153 | 2 |
| #127×D113 | 2 |
| #20298971 | 2 |
| #20298970 | 2 |
| #20298946 | 2 |
| #20298797 | 2 |
| #20298750 | 2 |
| #20298649 | 2 |
| #486×C113 | 2 |
| #3208 | 113 |