Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#16863434 | C2 | semidirect |
| 3. #22562418 | C2 | semidirect |
| 4. #22562401 | C2 | semidirect |
| 5. #22561997 | C2 | semidirect |
| 6. #22561922 | C2 | semidirect |
| 7. C67×#2112 | C2 | semidirect |
| 20. #16863224 | C22 | semidirect |
| 21. #16863222 | C22 | semidirect |
| 22. #16863201 | C22 | semidirect |
| 23. #16863198 | C22 | semidirect |
| 150. #2112 | D67 | semidirect |
| 151. C67 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569790 | 2 |
| C2×#16863434 | 2 |
| #22562418 | 2 |
| #22562401 | 2 |
| #22561997 | 2 |
| #22561922 | 2 |
| C67×#2112 | 2 |
| #33647 | 67 |