Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
656 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 227 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. #22560773 | C2 | semidirect |
| 4. #22560354 | C2 | semidirect |
| 5. #22560083 | C2 | semidirect |
| 7. C67×#1726 | C2 | semidirect |
| 123. #1726 | D67 | semidirect |
| 124. C67 | #21670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22563507 | 2 |
| #22560822 | 2 |
| #22560773 | 2 |
| #22560354 | 2 |
| #22560083 | 2 |
| #22559992 | 2 |
| C67×#1726 | 2 |
| #21670 | 67 |