Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#16813644 | C2 | semidirect |
| 2. #20299109 | C2 | semidirect |
| 3. #20298839 | C2 | semidirect |
| 4. #20298834 | C2 | semidirect |
| 5. #20298827 | C2 | semidirect |
| 6. #20298636 | C2 | semidirect |
| 7. #20298595 | C2 | semidirect |
| 8. C23×C8×C113 | C2 | semidirect |
| 11. C2×Dic452 | C22 | semidirect |
| 12. C2×#14268636 | C22 | semidirect |
| 13. C2×D904 | C22 | semidirect |
| 20. #16813556 | C22 | semidirect |
| 21. #16813554 | C22 | semidirect |
| 22. #16813547 | C22 | semidirect |
| 23. #16813544 | C22 | semidirect |
| 56. C2×C8×C113 | D4 | semidirect |
| 91. C22×C113 | #135 | semidirect |
| 107. C113 | #3050 | semidirect |
| 109. C23×C8 | D113 | semidirect |
| 157. C2×C8 | C22⋊D113 | semidirect |
| 200. C22 | #16813644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813644 | 2 |
| #20299109 | 2 |
| #20298839 | 2 |
| #20298834 | 2 |
| #20298827 | 2 |
| #20298636 | 2 |
| #20298595 | 2 |
| C23×C8×C113 | 2 |
| #3050 | 113 |