Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
418 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22560762 | C2 | semidirect |
| 5. #22560431 | C2 | semidirect |
| 6. #22558331 | C2 | semidirect |
| 7. C67×#2135 | C2 | semidirect |
| 194. #2135 | D67 | semidirect |
| 200. C67 | #13430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571076 | 2 |
| #22561900 | 2 |
| #22560762 | 2 |
| #22560754 | 2 |
| #22560431 | 2 |
| #22558331 | 2 |
| C67×#2135 | 2 |
| #13430 | 67 |