Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#14555499 | C2 | semidirect |
| 2. C2×#17984094 | C2 | semidirect |
| 3. #22577979 | C2 | semidirect |
| 5. #22577650 | C2 | semidirect |
| 6. #22577633 | C2 | semidirect |
| 7. #22577411 | C2 | semidirect |
| 8. #22577407 | C2 | semidirect |
| 9. #427×C137 | C2 | semidirect |
| 18. C2×#14555493 | C22 | semidirect |
| 19. C2×C8×D137 | C22 | semidirect |
| 25. #17984068 | C22 | semidirect |
| 28. #17984011 | C22 | semidirect |
| 33. #107×C137 | C22 | semidirect |
| 34. #106×C137 | C22 | semidirect |
| 62. C2×C8×C137 | D4 | semidirect |
| 120. C137 | #3057 | semidirect |
| 128. #427 | D137 | semidirect |
| 152. #107 | C2×D137 | semidirect |
| 153. #106 | C2×D137 | semidirect |
| 180. C2×C8 | D548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555499 | 2 |
| C2×#17984094 | 2 |
| #22577979 | 2 |
| #22577972 | 2 |
| #22577650 | 2 |
| #22577633 | 2 |
| #22577411 | 2 |
| #22577407 | 2 |
| #427×C137 | 2 |
| #3057 | 137 |