Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
426 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 426 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 |
|---|---|---|
| 1. C2×#16863226 | C2 | semidirect |
| 2. C2×#16863203 | C2 | semidirect |
| 3. C2×C16×Dic67 | C2 | semidirect |
| 4. #22561098 | C2 | semidirect |
| 17. C2×Q32×C67 | C4 | semidirect |
| 18. C2×SD32×C67 | C4 | semidirect |
| 19. C2×D16×C67 | C4 | semidirect |
| 130. C67 | #13241 | semidirect |
| 134. C2×Q32 | Dic67 | semidirect |
| 135. C2×SD32 | Dic67 | semidirect |
| 136. C2×D16 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863226 | 2 |
| C2×#16863203 | 2 |
| C2×C16×Dic67 | 2 |
| #22561098 | 2 |
| C2×#508×C67 | 2 |
| #13241 | 67 |