Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
478 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22561198 | C2 | semidirect |
| 4. #22558965 | C2 | semidirect |
| 5. #22558893 | C2 | semidirect |
| 7. C8×M16×C67 | C2 | semidirect |
| 157. C8×M16 | D67 | semidirect |
| 158. C67 | #9800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863743 | 2 |
| #22561198 | 2 |
| #22561049 | 2 |
| #22558965 | 2 |
| #22558893 | 2 |
| #22558876 | 2 |
| C8×M16×C67 | 2 |
| #9800 | 67 |