Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
392 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 3. #22558318 | C2 | semidirect |
| 4. #22558308 | C2 | semidirect |
| 8. #16863445 | C4 | semidirect |
| 131. C67 | #12875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863445 | 2 |
| #22560242 | 2 |
| #22558318 | 2 |
| #22558308 | 2 |
| C2×#349×C67 | 2 |
| #12875 | 67 |