Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 2. #22578113 | C2 | semidirect |
| 3. #22577808 | C2 | semidirect |
| 4. #22577743 | C2 | semidirect |
| 5. #22577715 | C2 | semidirect |
| 6. #22577698 | C2 | semidirect |
| 7. #22577693 | C2 | semidirect |
| 8. #22577646 | C2 | semidirect |
| 9. #22577482 | C2 | semidirect |
| 10. #22577442 | C2 | semidirect |
| 11. C4×SD16×C137 | C2 | semidirect |
| 121. C137 | #3357 | semidirect |
| 131. C4×SD16 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578118 | 2 |
| #22578113 | 2 |
| #22577808 | 2 |
| #22577743 | 2 |
| #22577715 | 2 |
| #22577698 | 2 |
| #22577693 | 2 |
| #22577646 | 2 |
| #22577482 | 2 |
| #22577442 | 2 |
| C4×SD16×C137 | 2 |
| #3357 | 137 |