Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 472 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. #22560019 | C2 | semidirect |
| 3. #22558800 | C2 | semidirect |
| 4. #22558718 | C2 | semidirect |
| 5. #22558103 | C2 | semidirect |
| 6. #22558082 | C2 | semidirect |
| 7. C67×#2971 | C2 | semidirect |
| 10. #16863681 | C4 | semidirect |
| 11. #16863676 | C4 | semidirect |
| 12. #16863596 | C4 | semidirect |
| 13. #16863591 | C4 | semidirect |
| 204. #2971 | D67 | semidirect |
| 210. C67 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570360 | 2 |
| #22560019 | 2 |
| #22558800 | 2 |
| #22558718 | 2 |
| #22558103 | 2 |
| #22558082 | 2 |
| C67×#2971 | 2 |
| #9162 | 67 |