Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
514 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22569339 | C2 | semidirect |
| 3. C4×#14523971 | C2 | semidirect |
| 4. #22558626 | C2 | semidirect |
| 5. #22558098 | C2 | semidirect |
| 6. #22558042 | C2 | semidirect |
| 7. C67×#1962 | C2 | semidirect |
| 10. #16863688 | C4 | semidirect |
| 11. #16863683 | C4 | semidirect |
| 12. #16863593 | C4 | semidirect |
| 13. #16863588 | C4 | semidirect |
| 179. Dic134 | #104 | semidirect |
| 219. #1962 | D67 | semidirect |
| 224. C67 | #8970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570263 | 2 |
| #22569339 | 2 |
| C4×#14523971 | 2 |
| #22558626 | 2 |
| #22558098 | 2 |
| #22558042 | 2 |
| C67×#1962 | 2 |
| #8970 | 67 |