Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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×#17984121 | C2 | semidirect |
| 2. C22×#14555499 | C2 | semidirect |
| 4. #22577880 | C2 | semidirect |
| 5. #22577626 | C2 | semidirect |
| 6. #22577604 | C2 | semidirect |
| 7. #22577409 | C2 | semidirect |
| 8. #22577400 | C2 | semidirect |
| 9. #424×C137 | C2 | semidirect |
| 14. C2×Dic548 | C22 | semidirect |
| 17. C2×#14555499 | C22 | semidirect |
| 22. C4×Dic274 | C22 | semidirect |
| 26. #17984013 | C22 | semidirect |
| 28. #17984010 | C22 | semidirect |
| 32. C4⋊C8×C137 | C22 | semidirect |
| 38. C2×Dic274 | D4 | semidirect |
| 116. C137 | #3043 | semidirect |
| 124. #424 | D137 | semidirect |
| 146. C4⋊C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984121 | 2 |
| C22×#14555499 | 2 |
| #22577972 | 2 |
| #22577880 | 2 |
| #22577626 | 2 |
| #22577604 | 2 |
| #22577409 | 2 |
| #22577400 | 2 |
| #424×C137 | 2 |
| #3043 | 137 |