Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 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. #22577476 | C2 | semidirect |
| 3. #22577473 | C2 | semidirect |
| 4. C8×D548 | C2 | semidirect |
| 5. #22577468 | C2 | semidirect |
| 6. #22577464 | C2 | semidirect |
| 7. #22577368 | C2 | semidirect |
| 8. C22⋊C8×D137 | C2 | semidirect |
| 9. #433×C137 | C2 | semidirect |
| 12. C2×#14555493 | C22 | semidirect |
| 15. C2×C8×D137 | C22 | semidirect |
| 22. C4⋊#11764040 | C22 | semidirect |
| 26. #17984000 | C22 | semidirect |
| 27. #17984000 | C22 | semidirect |
| 28. #17983999 | C22 | semidirect |
| 29. C4×#11764040 | C22 | semidirect |
| 31. C4⋊C8×C137 | C22 | semidirect |
| 33. #97×C137 | C22 | semidirect |
| 34. C4×C8×C137 | C22 | semidirect |
| 114. C137 | #2977 | semidirect |
| 122. #433 | D137 | semidirect |
| 139. C4⋊C8 | C2×D137 | semidirect |
| 147. #97 | C2×D137 | semidirect |
| 149. C4×C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577915 | 2 |
| #22577476 | 2 |
| #22577473 | 2 |
| C8×D548 | 2 |
| #22577468 | 2 |
| #22577464 | 2 |
| #22577368 | 2 |
| C22⋊C8×D137 | 2 |
| #433×C137 | 2 |
| #2977 | 137 |