Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
442 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 442 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×#16863209 | C2 | semidirect |
| 3. #22561805 | C2 | semidirect |
| 4. #22561120 | C2 | semidirect |
| 19. C2×D16×C67 | C4 | semidirect |
| 123. C67 | #13245 | semidirect |
| 128. 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×#16863209 | 2 |
| #22561805 | 2 |
| #22561120 | 2 |
| C22×D16×C67 | 2 |
| #13245 | 67 |