Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
554 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22561038 | C2 | semidirect |
| 3. #22561036 | C2 | semidirect |
| 4. C4×C8×Dic67 | C2 | semidirect |
| 5. #22558967 | C2 | semidirect |
| 6. #22558661 | C2 | semidirect |
| 7. C67×#1492 | C2 | semidirect |
| 9. #16863799 | C4 | semidirect |
| 10. #16863772 | C4 | semidirect |
| 11. #16863744 | C4 | semidirect |
| 12. #16863742 | C4 | semidirect |
| 89. C4×Dic67 | D8 | semidirect |
| 149. C67⋊C8 | #104 | semidirect |
| 183. #1492 | D67 | semidirect |
| 184. C67 | #9844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570784 | 2 |
| #22561038 | 2 |
| #22561036 | 2 |
| C4×C8×Dic67 | 2 |
| #22558967 | 2 |
| #22558661 | 2 |
| C67×#1492 | 2 |
| #9844 | 67 |