Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
938 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 155 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. #22571208 | C2 | semidirect |
| 3. #22559524 | C2 | semidirect |
| 4. #22558836 | C2 | semidirect |
| 5. #22558806 | C2 | semidirect |
| 6. C67×#3166 | C2 | semidirect |
| 14. #16863788 | C22 | semidirect |
| 15. #16863758 | C22 | semidirect |
| 20. #16863138 | C22 | semidirect |
| 21. #16863135 | C22 | semidirect |
| 24. #501×C67 | C22 | semidirect |
| 154. #3166 | D67 | semidirect |
| 158. C67 | #19006 | semidirect |
| 168. #501 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864144 | 2 |
| #22571208 | 2 |
| #22559524 | 2 |
| #22558836 | 2 |
| #22558806 | 2 |
| C67×#3166 | 2 |
| #19006 | 67 |