Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
868 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 868 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22561012 | C2 | semidirect |
| 3. #22560210 | C2 | semidirect |
| 4. C2×#16863123 | C2 | semidirect |
| 5. C2×#333×C67 | C2 | semidirect |
| 8. #16864112 | C4 | semidirect |
| 169. C2×#333 | D67 | semidirect |
| 171. C67 | #8452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864112 | 2 |
| #22561012 | 2 |
| #22560210 | 2 |
| C2×#16863123 | 2 |
| C2×#333×C67 | 2 |
| #8452 | 67 |