Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
412 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16863226 | C2 | semidirect |
| 3. C2×#16863209 | C2 | semidirect |
| 4. #22561822 | C2 | semidirect |
| 5. #22560274 | C2 | semidirect |
| 6. #22558317 | C2 | semidirect |
| 7. C2×#357×C67 | C2 | semidirect |
| 174. C2×#357 | D67 | semidirect |
| 178. C67 | #13393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863663 | 2 |
| C2×#16863226 | 2 |
| C2×#16863209 | 2 |
| #22561822 | 2 |
| #22560274 | 2 |
| #22558317 | 2 |
| C2×#357×C67 | 2 |
| #13393 | 67 |