Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
456 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#16863764 | C2 | semidirect |
| 5. #22558566 | C2 | semidirect |
| 6. #22558107 | C2 | semidirect |
| 7. C67×#1556 | C2 | semidirect |
| 172. #1556 | D67 | semidirect |
| 176. C67 | #10134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571401 | 2 |
| #22571337 | 2 |
| C2×#16863764 | 2 |
| #22558821 | 2 |
| #22558566 | 2 |
| #22558107 | 2 |
| C67×#1556 | 2 |
| #10134 | 67 |