Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. #22558565 | C2 | semidirect |
| 5. #22558078 | C2 | semidirect |
| 6. #22558060 | C2 | semidirect |
| 7. C67×#1528 | C2 | semidirect |
| 206. #1528 | D67 | semidirect |
| 211. C67 | #9245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863693 | 2 |
| #22569246 | 2 |
| #22558653 | 2 |
| #22558565 | 2 |
| #22558078 | 2 |
| #22558060 | 2 |
| C67×#1528 | 2 |
| #9245 | 67 |