Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #22577880 | C2 | semidirect |
| 4. #22577500 | C2 | semidirect |
| 5. #22577494 | C2 | semidirect |
| 6. #22577439 | C2 | semidirect |
| 7. #22577413 | C2 | semidirect |
| 8. #22577361 | C2 | semidirect |
| 11. C2×#14555498 | C4 | semidirect |
| 16. #17984053 | C22 | semidirect |
| 23. #17984021 | C22 | semidirect |
| 24. #17984019 | C22 | semidirect |
| 25. #17984013 | C22 | semidirect |
| 26. #17983998 | C22 | semidirect |
| 27. C8×Dic137 | C22 | semidirect |
| 34. C2×Dic274 | C2×C4 | semidirect |
| 38. #14555498 | C2×C4 | semidirect |
| 39. #14555498 | C2×C4 | semidirect |
| 40. C2×#11764040 | C2×C4 | semidirect |
| 103. C137 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555498 | 2 |
| #22577880 | 2 |
| #22577878 | 2 |
| #22577500 | 2 |
| #22577494 | 2 |
| #22577439 | 2 |
| #22577413 | 2 |
| #22577361 | 2 |
| #418×C137 | 2 |
| #2949 | 137 |