Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20299398 | C2 | semidirect |
| 2. C2×#16813648 | C2 | semidirect |
| 3. C2×#16813648 | C2 | semidirect |
| 4. #20299364 | C2 | semidirect |
| 5. #20298867 | C2 | semidirect |
| 6. #20298860 | C2 | semidirect |
| 7. #20298646 | C2 | semidirect |
| 8. #20298580 | C2 | semidirect |
| 9. C2×#100×C113 | C2 | semidirect |
| 13. #16813655 | C22 | semidirect |
| 15. #16813650 | C22 | semidirect |
| 22. C2×#14268635 | C22 | semidirect |
| 24. C2×#14268632 | C22 | semidirect |
| 25. #16813630 | C22 | semidirect |
| 30. #16813557 | C22 | semidirect |
| 31. #16813540 | C22 | semidirect |
| 32. #16813538 | C22 | semidirect |
| 36. #100×C113 | C22 | semidirect |
| 148. C113 | #3068 | semidirect |
| 157. C2×#100 | D113 | semidirect |
| 184. #100 | C2×D113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299398 | 2 |
| C2×#16813648 | 2 |
| #20299364 | 2 |
| #20298867 | 2 |
| #20298860 | 2 |
| #20298646 | 2 |
| #20298580 | 2 |
| C2×#100×C113 | 2 |
| #3068 | 113 |