Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 680 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 |
|---|---|---|
| 3. #22569077 | C2 | semidirect |
| 4. #22562273 | C2 | semidirect |
| 5. #22562257 | C2 | semidirect |
| 6. #22561967 | C2 | semidirect |
| 7. #22561929 | C2 | semidirect |
| 9. C22×Q32×C67 | C2 | semidirect |
| 173. C22×Q32 | D67 | semidirect |
| 181. C67 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863837 | 2 |
| #22570698 | 2 |
| #22569077 | 2 |
| #22562273 | 2 |
| #22562257 | 2 |
| #22561967 | 2 |
| #22561929 | 2 |
| #22561917 | 2 |
| C22×Q32×C67 | 2 |
| #33588 | 67 |