Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. C2×#16813581 | C2 | semidirect |
| 3. #20298923 | C2 | semidirect |
| 4. #20298917 | C2 | semidirect |
| 5. #20298912 | C2 | semidirect |
| 6. #20298640 | C2 | semidirect |
| 7. #20298604 | C2 | semidirect |
| 8. #407×C113 | C2 | semidirect |
| 18. #16813581 | C22 | semidirect |
| 20. C2×C4⋊Dic113 | C22 | semidirect |
| 21. C2×C4⋊Dic113 | C22 | semidirect |
| 25. #16813556 | C22 | semidirect |
| 26. #16813554 | C22 | semidirect |
| 27. #16813544 | C22 | semidirect |
| 28. #16813544 | C22 | semidirect |
| 31. C22⋊C8×C113 | C22 | semidirect |
| 32. C22⋊C8×C113 | C22 | semidirect |
| 126. C113 | #3094 | semidirect |
| 134. #407 | D113 | semidirect |
| 157. C22⋊C8 | C2×D113 | semidirect |
| 158. C22⋊C8 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813596 | 2 |
| C2×#16813581 | 2 |
| #20298923 | 2 |
| #20298917 | 2 |
| #20298912 | 2 |
| #20298640 | 2 |
| #20298604 | 2 |
| #407×C113 | 2 |
| #3094 | 113 |