Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #22577747 | C2 | semidirect |
| 4. #22577735 | C2 | semidirect |
| 5. #22577695 | C2 | semidirect |
| 6. #22577685 | C2 | semidirect |
| 7. #22577662 | C2 | semidirect |
| 8. C4×Dic548 | C2 | semidirect |
| 10. #22577442 | C2 | semidirect |
| 11. #498×C137 | C2 | semidirect |
| 116. C137 | #3356 | semidirect |
| 120. #498 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578127 | 2 |
| #22578114 | 2 |
| #22577747 | 2 |
| #22577735 | 2 |
| #22577695 | 2 |
| #22577685 | 2 |
| #22577662 | 2 |
| C4×Dic548 | 2 |
| #22577482 | 2 |
| #22577442 | 2 |
| #498×C137 | 2 |
| #3356 | 137 |