Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
380 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22558937 | C2 | semidirect |
| 5. #22558803 | C2 | semidirect |
| 6. #22558080 | C2 | semidirect |
| 7. C67×#1569 | C2 | semidirect |
| 183. #1569 | D67 | semidirect |
| 188. C67 | #10498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571214 | 2 |
| #22561056 | 2 |
| #22558937 | 2 |
| #22558806 | 2 |
| #22558803 | 2 |
| #22558080 | 2 |
| C67×#1569 | 2 |
| #10498 | 67 |