Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 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. #22577878 | C2 | semidirect |
| 3. #22577877 | C2 | semidirect |
| 4. #22577512 | C2 | semidirect |
| 5. #22577483 | C2 | semidirect |
| 6. #22577439 | C2 | semidirect |
| 7. #22577409 | C2 | semidirect |
| 8. #22577361 | C2 | semidirect |
| 9. #418×C137 | C2 | semidirect |
| 11. C2×#14555495 | C4 | semidirect |
| 17. D4×Dic137 | C22 | semidirect |
| 18. #17984050 | C22 | semidirect |
| 23. #17984021 | C22 | semidirect |
| 24. #17984019 | C22 | semidirect |
| 25. #17984010 | C22 | semidirect |
| 26. #17983998 | C22 | semidirect |
| 27. C8×Dic137 | C22 | semidirect |
| 31. #102×C137 | C22 | semidirect |
| 35. C2×D548 | C2×C4 | semidirect |
| 39. #14555495 | C2×C4 | semidirect |
| 40. #14555495 | C2×C4 | semidirect |
| 41. C2×#11764040 | C2×C4 | semidirect |
| 55. C2×D4×C137 | C2×C4 | semidirect |
| 108. C137 | #2948 | semidirect |
| 117. #418 | D137 | semidirect |
| 138. #102 | C2×D137 | semidirect |
| 149. C2×D4 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555495 | 2 |
| #22577878 | 2 |
| #22577877 | 2 |
| #22577512 | 2 |
| #22577483 | 2 |
| #22577439 | 2 |
| #22577409 | 2 |
| #22577361 | 2 |
| #418×C137 | 2 |
| #2948 | 137 |