Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
448 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 103 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×#16863153 | C2 | semidirect |
| 3. #22558198 | C2 | semidirect |
| 4. #22558195 | C2 | semidirect |
| 5. C2×#349×C67 | C2 | semidirect |
| 6. C2×#14524065 | C4 | semidirect |
| 9. #16863654 | C4 | semidirect |
| 11. #16863649 | C4 | semidirect |
| 15. #16863434 | C4 | semidirect |
| 26. C2×Dic268 | C2×C4 | semidirect |
| 28. C2×D536 | C2×C4 | semidirect |
| 46. #14523975 | C2×C4 | semidirect |
| 47. #14523975 | C2×C4 | semidirect |
| 194. C2×#349 | D67 | semidirect |
| 198. C67 | #11685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569818 | 2 |
| C2×#16863153 | 2 |
| #22558198 | 2 |
| #22558195 | 2 |
| C2×#349×C67 | 2 |
| #11685 | 67 |