Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
566 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 1. #22571399 | C2 | semidirect |
| 3. #22565376 | C2 | semidirect |
| 4. #22561128 | C2 | semidirect |
| 5. #22558653 | C2 | semidirect |
| 6. #22558064 | C2 | semidirect |
| 7. C67×#1528 | C2 | semidirect |
| 221. #1528 | D67 | semidirect |
| 224. C67 | #10005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571399 | 2 |
| #22570301 | 2 |
| #22565376 | 2 |
| #22561128 | 2 |
| #22558653 | 2 |
| #22558064 | 2 |
| C67×#1528 | 2 |
| #10005 | 67 |