Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
416 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22561983 | C2 | semidirect |
| 5. #22558323 | C2 | semidirect |
| 6. #22558295 | C2 | semidirect |
| 7. C67×#1953 | C2 | semidirect |
| 18. #16863208 | C4 | semidirect |
| 38. #14523983 | C2×C4 | semidirect |
| 53. #108×C67 | C2×C4 | semidirect |
| 142. #1953 | D67 | semidirect |
| 145. C67 | #12953 | semidirect |
| 188. #108 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569062 | 2 |
| #22561983 | 2 |
| C2×#16863208 | 2 |
| #22558323 | 2 |
| #22558295 | 2 |
| C67×#1953 | 2 |
| #12953 | 67 |