Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
408 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#16863218 | C2 | semidirect |
| 5. #22558319 | C2 | semidirect |
| 6. #22558318 | C2 | semidirect |
| 7. C2×#365×C67 | C2 | semidirect |
| 18. #16863177 | C4 | semidirect |
| 155. C2×#365 | D67 | semidirect |
| 160. C67 | #12931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863443 | 2 |
| C2×#16863218 | 2 |
| C2×#16863177 | 2 |
| #22560239 | 2 |
| #22558319 | 2 |
| #22558318 | 2 |
| C2×#365×C67 | 2 |
| #12931 | 67 |