Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
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×#17984003 | C2 | semidirect |
| 3. #22577191 | C2 | direct (N × H) |
| 4. C2×#100×C137 | C2 | semidirect |
| 5. C24×D137 | C4 | semidirect |
| 9. #17984056 | C4 | semidirect |
| 12. C2×C22⋊Dic137 | C4 | semidirect |
| 15. #17984003 | C22 | semidirect |
| 19. #100×C137 | C22 | semidirect |
| 25. C23×D137 | C2×C4 | semidirect |
| 34. C22⋊Dic137 | C2×C4 | semidirect |
| 121. C2×C137 | AΣL(1,𝔽16) | semidirect |
| 124. C137 | C2×AΣL(1,𝔽16) | semidirect |
| 127. C2×#100 | D137 | semidirect |
| 142. #100 | C2×D137 | semidirect |
| 247. C2 | #22577191 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984056 | 2 |
| C2×#17984003 | 2 |
| #22577191 | 2 |
| C2×#100×C137 | 2 |
| C2×AΣL(1,𝔽16) | 137 |