Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
390 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 87 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. #22561981 | C2 | semidirect |
| 3. #22561937 | C2 | semidirect |
| 4. #22561822 | C2 | semidirect |
| 5. #22560260 | C2 | semidirect |
| 6. #22558303 | C2 | semidirect |
| 7. C67×#2138 | C2 | semidirect |
| 178. #2138 | D67 | semidirect |
| 182. C67 | #13406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569925 | 2 |
| #22561981 | 2 |
| #22561937 | 2 |
| #22561822 | 2 |
| #22560260 | 2 |
| #22558303 | 2 |
| C67×#2138 | 2 |
| #13406 | 67 |