Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. C2×#16813537 | C2 | semidirect |
| 3. #20298386 | C2 | direct (N × H) |
| 4. C2×#100×C113 | C2 | semidirect |
| 5. C24×D113 | C4 | semidirect |
| 9. #16813590 | C4 | semidirect |
| 12. C2×C22⋊Dic113 | C4 | semidirect |
| 15. #16813537 | C22 | semidirect |
| 19. #100×C113 | C22 | semidirect |
| 25. C23×D113 | C2×C4 | semidirect |
| 34. C22⋊Dic113 | C2×C4 | semidirect |
| 121. C2×C113 | AΣL(1,𝔽16) | semidirect |
| 125. C113 | C2×AΣL(1,𝔽16) | semidirect |
| 127. C2×#100 | D113 | semidirect |
| 142. #100 | C2×D113 | semidirect |
| 247. C2 | #20298386 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813590 | 2 |
| C2×#16813537 | 2 |
| #20298386 | 2 |
| C2×#100×C113 | 2 |
| C2×AΣL(1,𝔽16) | 113 |