Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
728 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22570928 | C2 | semidirect |
| 3. #22570605 | C2 | semidirect |
| 4. #22559863 | C2 | semidirect |
| 5. #22559857 | C2 | semidirect |
| 6. #22559851 | C2 | semidirect |
| 7. #22559822 | C2 | semidirect |
| 8. #22558512 | C2 | semidirect |
| 9. C67×#3139 | C2 | semidirect |
| 162. #3139 | D67 | semidirect |
| 168. C67 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570947 | 2 |
| #22570928 | 2 |
| #22570605 | 2 |
| #22559863 | 2 |
| #22559857 | 2 |
| #22559851 | 2 |
| #22559822 | 2 |
| #22558512 | 2 |
| C67×#3139 | 2 |
| #19754 | 67 |