Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
724 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22560133 | C2 | semidirect |
| 4. #22558573 | C2 | semidirect |
| 6. #22558097 | C2 | semidirect |
| 7. C2×#451×C67 | C2 | semidirect |
| 217. C2×#451 | D67 | semidirect |
| 223. C67 | #9989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571011 | 2 |
| C2×#16863535 | 2 |
| #22560133 | 2 |
| #22558573 | 2 |
| #22558568 | 2 |
| #22558097 | 2 |
| C2×#451×C67 | 2 |
| #9989 | 67 |