Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22577271 | C2 | semidirect |
| 3. #22577141 | C2 | semidirect |
| 5. #431×C137 | C2 | semidirect |
| 7. #17984080 | C4 | semidirect |
| 8. #17984076 | C4 | semidirect |
| 12. C4×Dic274 | C4 | semidirect |
| 13. C4×D548 | C4 | semidirect |
| 92. C137 | #1521 | semidirect |
| 95. #431 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577937 | 2 |
| #22577271 | 2 |
| #22577141 | 2 |
| #22577138 | 2 |
| #431×C137 | 2 |
| #1521 | 137 |