Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. #20299148 | C2 | semidirect |
| 2. C2×#16813619 | C2 | semidirect |
| 3. #20298975 | C2 | semidirect |
| 4. #20298945 | C2 | semidirect |
| 5. #20298794 | C2 | semidirect |
| 6. #20298734 | C2 | semidirect |
| 7. #431×C113 | C2 | semidirect |
| 12. C2×D904 | C22 | semidirect |
| 13. #16813622 | C22 | semidirect |
| 18. #16813619 | C22 | semidirect |
| 23. C4×D452 | C22 | semidirect |
| 24. #16813544 | C22 | semidirect |
| 26. C4⋊C8×C113 | C22 | semidirect |
| 28. C4×C8×C113 | C22 | semidirect |
| 67. C2×C4×C113 | D8 | semidirect |
| 113. C113 | #3205 | semidirect |
| 120. #431 | D113 | semidirect |
| 138. C4⋊C8 | C2×D113 | semidirect |
| 141. C4×C8 | C2×D113 | semidirect |
| 193. C2×C4 | D904 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299148 | 2 |
| C2×#16813619 | 2 |
| #20298975 | 2 |
| #20298945 | 2 |
| #20298794 | 2 |
| #20298734 | 2 |
| #431×C113 | 2 |
| #3205 | 113 |