Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22560293 | C2 | semidirect |
| 4. #22560287 | C2 | semidirect |
| 5. #22558115 | C2 | semidirect |
| 6. #22558085 | C2 | semidirect |
| 9. #16863729 | C4 | semidirect |
| 11. #16863712 | C4 | semidirect |
| 224. C67 | #9522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570129 | 2 |
| #22569257 | 2 |
| #22560293 | 2 |
| #22560287 | 2 |
| #22558115 | 2 |
| #22558085 | 2 |
| C67×#1513 | 2 |
| #9522 | 67 |