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. C2×#16813619 | C2 | semidirect |
| 2. #20298974 | C2 | semidirect |
| 3. #20298946 | C2 | semidirect |
| 4. #20298793 | C2 | semidirect |
| 5. #20298731 | C2 | semidirect |
| 6. #20298651 | C2 | semidirect |
| 7. #532×C113 | C2 | semidirect |
| 11. C2×#14268632 | C22 | semidirect |
| 16. C4⋊#11744751 | C22 | semidirect |
| 17. #16813542 | C22 | semidirect |
| 19. C4×#11744751 | C22 | semidirect |
| 21. C4⋊Q8×C113 | C22 | semidirect |
| 22. #127×C113 | C22 | semidirect |
| 27. C4×D4×C113 | C22 | semidirect |
| 74. C2×C4×C113 | D8 | semidirect |
| 113. C113 | #3205 | semidirect |
| 114. #532 | D113 | semidirect |
| 126. C4⋊Q8 | C2×D113 | semidirect |
| 131. #127 | C2×D113 | semidirect |
| 136. C4×D4 | C2×D113 | semidirect |
| 193. C2×C4 | #14268632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813619 | 2 |
| #20298974 | 2 |
| #20298946 | 2 |
| #20298793 | 2 |
| #20298731 | 2 |
| #20298651 | 2 |
| #532×C113 | 2 |
| #3205 | 113 |