Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 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. #20299150 | C2 | semidirect |
| 3. #20298969 | C2 | semidirect |
| 4. #20298943 | C2 | semidirect |
| 5. #20298797 | C2 | semidirect |
| 6. #20298796 | C2 | semidirect |
| 7. #20298751 | C2 | semidirect |
| 8. #20298749 | C2 | semidirect |
| 9. #20298748 | C2 | semidirect |
| 10. #20298648 | C2 | semidirect |
| 11. #450×C113 | C2 | semidirect |
| 15. C2×#14268636 | C22 | semidirect |
| 16. C2×#14268635 | C22 | semidirect |
| 17. C2×#14268634 | C22 | semidirect |
| 18. #16813621 | C22 | semidirect |
| 19. #16813620 | C22 | semidirect |
| 27. Q8×Dic113 | C22 | semidirect |
| 29. #16813587 | C22 | semidirect |
| 32. #16813551 | C22 | semidirect |
| 33. #16813544 | C22 | semidirect |
| 34. #16813543 | C22 | semidirect |
| 35. #16813542 | C22 | semidirect |
| 37. C8×Dic113 | C22 | semidirect |
| 39. C2×SD16×C113 | C22 | semidirect |
| 41. #102×C113 | C22 | semidirect |
| 111. C2×Dic113 | SD16 | semidirect |
| 152. C113 | #3208 | semidirect |
| 162. #450 | D113 | semidirect |
| 171. C2×SD16 | C2×D113 | semidirect |
| 191. #102 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299150 | 2 |
| C2×#16813618 | 2 |
| #20298969 | 2 |
| #20298943 | 2 |
| #20298797 | 2 |
| #20298796 | 2 |
| #20298751 | 2 |
| #20298749 | 2 |
| #20298748 | 2 |
| #20298648 | 2 |
| #450×C113 | 2 |
| #3208 | 113 |