Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16813580 | C2 | semidirect |
| 3. #20298925 | C2 | direct (N × H) |
| 4. C2×#16813553 | C2 | semidirect |
| 5. C2×#16813544 | C2 | semidirect |
| 6. C2×#16813542 | C2 | semidirect |
| 7. C2×#16813534 | C2 | semidirect |
| 8. C2×#107×C113 | C2 | semidirect |
| 16. #16813580 | C22 | semidirect |
| 21. #16813553 | C22 | semidirect |
| 22. #16813544 | C22 | semidirect |
| 23. #16813542 | C22 | semidirect |
| 24. #16813534 | C22 | semidirect |
| 28. #107×C113 | C22 | semidirect |
| 108. C2×C113 | #482 | semidirect |
| 115. C113 | C2×#482 | semidirect |
| 119. C2×#107 | D113 | semidirect |
| 139. #107 | C2×D113 | semidirect |
| 225. C2 | #20298925 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813597 | 2 |
| C2×#16813580 | 2 |
| #20298925 | 2 |
| C2×#16813553 | 2 |
| C2×#16813544 | 2 |
| C2×#16813542 | 2 |
| C2×#16813534 | 2 |
| C2×#107×C113 | 2 |
| C2×#482 | 113 |