Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
770 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 255 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 |
|---|---|---|
| 3. #22560383 | C2 | semidirect |
| 4. #22560350 | C2 | semidirect |
| 6. #22560114 | C2 | semidirect |
| 7. C67×#1838 | C2 | semidirect |
| 112. #1838 | D67 | semidirect |
| 115. C67 | #20830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568841 | 2 |
| C2×#97×D67 | 2 |
| #22560383 | 2 |
| #22560350 | 2 |
| #22560246 | 2 |
| #22560114 | 2 |
| C67×#1838 | 2 |
| #20830 | 67 |