Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22577754 | C2 | semidirect |
| 4. #22577740 | C2 | semidirect |
| 5. #22577698 | C2 | semidirect |
| 6. #22577643 | C2 | semidirect |
| 7. #22577613 | C2 | semidirect |
| 8. #22577557 | C2 | semidirect |
| 10. #103×D137 | C2 | semidirect |
| 11. C4×Q16×C137 | C2 | semidirect |
| 81. D548 | Q16 | semidirect |
| 122. C137 | #3299 | semidirect |
| 132. C4×Q16 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578113 | 2 |
| Q8×D548 | 2 |
| #22577754 | 2 |
| #22577740 | 2 |
| #22577698 | 2 |
| #22577643 | 2 |
| #22577613 | 2 |
| #22577557 | 2 |
| C8×D548 | 2 |
| #103×D137 | 2 |
| C4×Q16×C137 | 2 |
| #3299 | 137 |