Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 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. #20299155 | C2 | semidirect |
| 3. #20298929 | C2 | semidirect |
| 4. #20298889 | C2 | semidirect |
| 5. #20298804 | C2 | semidirect |
| 7. C4×#14268636 | C2 | semidirect |
| 8. #431×C113 | C2 | semidirect |
| 12. #16813622 | C22 | semidirect |
| 13. #16813622 | C22 | semidirect |
| 18. C4×Dic226 | C22 | semidirect |
| 26. #16813554 | C22 | semidirect |
| 27. #16813547 | C22 | semidirect |
| 30. C4⋊C8×C113 | C22 | semidirect |
| 32. C4×C8×C113 | C22 | semidirect |
| 71. C2×C4×C113 | SD16 | semidirect |
| 113. C113 | #3101 | semidirect |
| 121. #431 | D113 | semidirect |
| 141. C4⋊C8 | C2×D113 | semidirect |
| 145. C4×C8 | C2×D113 | semidirect |
| 195. C2×C4 | #14268636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299155 | 2 |
| C2×C4×D452 | 2 |
| #20298929 | 2 |
| #20298889 | 2 |
| #20298804 | 2 |
| #20298751 | 2 |
| C4×#14268636 | 2 |
| #431×C113 | 2 |
| #3101 | 113 |