Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#17984116 | C2 | semidirect |
| 2. #22577953 | C2 | semidirect |
| 3. C2×C4×D548 | C2 | semidirect |
| 4. #22577619 | C2 | semidirect |
| 5. #22577609 | C2 | semidirect |
| 6. #22577599 | C2 | semidirect |
| 7. #22577405 | C2 | semidirect |
| 8. #423×C137 | C2 | semidirect |
| 15. #17984088 | C22 | semidirect |
| 16. #17984085 | C22 | semidirect |
| 17. #17984076 | C22 | semidirect |
| 28. #17984013 | C22 | semidirect |
| 29. #17984010 | C22 | semidirect |
| 32. C4⋊C8×C137 | C22 | semidirect |
| 33. C4⋊C8×C137 | C22 | semidirect |
| 42. C2×D548 | D4 | semidirect |
| 118. C4×C137 | AGL(1,ℤ/8) | semidirect |
| 129. C137 | #3036 | semidirect |
| 137. #423 | D137 | semidirect |
| 160. C4⋊C8 | C2×D137 | semidirect |
| 161. C4⋊C8 | C2×D137 | semidirect |
| 250. C4 | #17984116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984116 | 2 |
| #22577953 | 2 |
| C2×C4×D548 | 2 |
| #22577619 | 2 |
| #22577609 | 2 |
| #22577599 | 2 |
| #22577405 | 2 |
| #423×C137 | 2 |
| #3036 | 137 |