Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
402 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 19. C2×Q32×C67 | C4 | semidirect |
| 118. C67 | #13244 | semidirect |
| 123. C2×Q32 | 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×#16863212 | 2 |
| #22561805 | 2 |
| #22561125 | 2 |
| C22×Q32×C67 | 2 |
| #13244 | 67 |