Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 1. #22578113 | C2 | semidirect |
| 2. #22577757 | C2 | semidirect |
| 3. #22577749 | C2 | semidirect |
| 4. #22577703 | C2 | semidirect |
| 5. #22577698 | C2 | semidirect |
| 6. #22577615 | C2 | semidirect |
| 8. Q8×#11764040 | C2 | semidirect |
| 9. C4×#14555497 | C2 | semidirect |
| 10. C4×#14555495 | C2 | semidirect |
| 11. #559×C137 | C2 | semidirect |
| 122. C137 | #3361 | semidirect |
| 124. #559 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578113 | 2 |
| #22577757 | 2 |
| #22577749 | 2 |
| #22577703 | 2 |
| #22577698 | 2 |
| #22577615 | 2 |
| #22577595 | 2 |
| Q8×#11764040 | 2 |
| C4×#14555497 | 2 |
| C4×#14555495 | 2 |
| #559×C137 | 2 |
| #3361 | 137 |