Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22569263 | C2 | semidirect |
| 3. #22558714 | C2 | semidirect |
| 4. C2×#16863130 | C2 | semidirect |
| 5. #22558096 | C2 | semidirect |
| 6. #22558051 | C2 | semidirect |
| 7. C67×#1471 | C2 | semidirect |
| 9. #16863731 | C4 | semidirect |
| 11. #16863714 | C4 | semidirect |
| 14. #16863547 | C4 | semidirect |
| 16. #16863530 | C4 | semidirect |
| 250. #1471 | D67 | semidirect |
| 253. C67 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570974 | 2 |
| #22569263 | 2 |
| #22558714 | 2 |
| C2×#16863130 | 2 |
| #22558096 | 2 |
| #22558051 | 2 |
| C67×#1471 | 2 |
| #9264 | 67 |