Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22577772 | C2 | semidirect |
| 4. #22577763 | C2 | semidirect |
| 5. #22577758 | C2 | semidirect |
| 6. #22577754 | C2 | semidirect |
| 7. #22577413 | C2 | semidirect |
| 10. C2×#17984013 | C2 | semidirect |
| 11. #405×C137 | C2 | semidirect |
| 127. C137 | #3137 | semidirect |
| 139. #405 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578031 | 2 |
| #22577979 | 2 |
| #22577772 | 2 |
| #22577763 | 2 |
| #22577758 | 2 |
| #22577754 | 2 |
| #22577413 | 2 |
| #22577405 | 2 |
| #22577400 | 2 |
| C2×#17984013 | 2 |
| #405×C137 | 2 |
| #3137 | 137 |