Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
464 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22569271 | C2 | semidirect |
| 3. #22558737 | C2 | semidirect |
| 4. #22558568 | C2 | semidirect |
| 5. #22558117 | C2 | semidirect |
| 6. #22558086 | C2 | semidirect |
| 7. C67×#1516 | C2 | semidirect |
| 9. #16863724 | C4 | semidirect |
| 11. #16863707 | C4 | semidirect |
| 14. #16863546 | C4 | semidirect |
| 16. #16863529 | C4 | semidirect |
| 228. #1516 | D67 | semidirect |
| 233. C67 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571019 | 2 |
| #22569271 | 2 |
| #22558737 | 2 |
| #22558568 | 2 |
| #22558117 | 2 |
| #22558086 | 2 |
| C67×#1516 | 2 |
| #9332 | 67 |