Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
342 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22577799 | C2 | semidirect |
| 3. #22577744 | C2 | semidirect |
| 4. #22577731 | C2 | semidirect |
| 5. #22577698 | C2 | semidirect |
| 6. #22577685 | C2 | semidirect |
| 7. #22577659 | C2 | semidirect |
| 8. C4×#14555500 | C2 | semidirect |
| 10. #22577446 | C2 | semidirect |
| 116. C137 | #3356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578110 | 2 |
| #22577799 | 2 |
| #22577744 | 2 |
| #22577731 | 2 |
| #22577698 | 2 |
| #22577685 | 2 |
| #22577659 | 2 |
| C4×#14555500 | 2 |
| #22577481 | 2 |
| #22577446 | 2 |
| #556×C137 | 2 |
| #3356 | 137 |