Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22578031 | C2 | semidirect |
| 3. #22577770 | C2 | semidirect |
| 4. #22577764 | C2 | semidirect |
| 5. #22577759 | C2 | semidirect |
| 6. #22577752 | C2 | semidirect |
| 9. C2×#17984012 | C2 | semidirect |
| 10. #22577361 | C2 | semidirect |
| 11. #419×C137 | C2 | semidirect |
| 127. C137 | #3137 | semidirect |
| 135. #419 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578031 | 2 |
| #22577977 | 2 |
| #22577770 | 2 |
| #22577764 | 2 |
| #22577759 | 2 |
| #22577752 | 2 |
| #22577405 | 2 |
| #22577397 | 2 |
| C2×#17984012 | 2 |
| #22577361 | 2 |
| #419×C137 | 2 |
| #3137 | 137 |