Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
458 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 2. #22560381 | C2 | semidirect |
| 3. #22558893 | C2 | semidirect |
| 4. #22558889 | C2 | semidirect |
| 7. C67×#1452 | C2 | semidirect |
| 150. #1452 | D67 | semidirect |
| 151. C67 | #9774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863743 | 2 |
| #22560381 | 2 |
| #22558893 | 2 |
| #22558889 | 2 |
| #22558876 | 2 |
| C67×#1452 | 2 |
| #9774 | 67 |