Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
470 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 89 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. C22⋊C16×D67 | C2 | semidirect |
| 3. #22560237 | C2 | semidirect |
| 4. #22558219 | C2 | semidirect |
| 5. #22558218 | C2 | semidirect |
| 6. #22558217 | C2 | semidirect |
| 7. C67×#1347 | C2 | semidirect |
| 8. C2×D8×D67 | C4 | semidirect |
| 12. #16863633 | C4 | semidirect |
| 16. #16863629 | C4 | semidirect |
| 18. #107×D67 | C4 | semidirect |
| 21. C22⋊(C67⋊C16) | C22 | semidirect |
| 23. #16863159 | C22 | semidirect |
| 25. C22⋊C16×C67 | C22 | semidirect |
| 26. #340×C67 | C22 | semidirect |
| 209. #1347 | D67 | semidirect |
| 210. C67 | #11886 | semidirect |
| 227. C22⋊C16 | C2×D67 | semidirect |
| 229. #340 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #466×D67 | 2 |
| C22⋊C16×D67 | 2 |
| #22560237 | 2 |
| #22558219 | 2 |
| #22558218 | 2 |
| #22558217 | 2 |
| C67×#1347 | 2 |
| #11886 | 67 |