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. #22577801 | C2 | semidirect |
| 4. #22577742 | C2 | semidirect |
| 5. #22577732 | C2 | semidirect |
| 6. #22577698 | C2 | semidirect |
| 7. #22577688 | C2 | semidirect |
| 8. #22577658 | C2 | semidirect |
| 10. #22577444 | C2 | semidirect |
| 11. C4×Q16×C137 | C2 | semidirect |
| 116. C137 | #3356 | semidirect |
| 126. C4×Q16 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578126 | 2 |
| #22578113 | 2 |
| #22577801 | 2 |
| #22577742 | 2 |
| #22577732 | 2 |
| #22577698 | 2 |
| #22577688 | 2 |
| #22577658 | 2 |
| #22577482 | 2 |
| #22577444 | 2 |
| C4×Q16×C137 | 2 |
| #3356 | 137 |