Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
590 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22572491 | C2 | semidirect |
| 3. #22559760 | C2 | semidirect |
| 4. #22559753 | C2 | semidirect |
| 5. #22559462 | C2 | semidirect |
| 6. #22559455 | C2 | semidirect |
| 7. #22559107 | C2 | semidirect |
| 9. C67×#1710 | C2 | semidirect |
| 168. #1710 | D67 | semidirect |
| 175. C67 | #20306 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22572932 | 2 |
| #22572491 | 2 |
| #22559760 | 2 |
| #22559753 | 2 |
| #22559462 | 2 |
| #22559455 | 2 |
| #22559107 | 2 |
| #22559095 | 2 |
| C67×#1710 | 2 |
| #20306 | 67 |