Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22562011 | C2 | semidirect |
| 3. #22562006 | C2 | semidirect |
| 4. #22558165 | C2 | semidirect |
| 5. D4⋊(C67⋊C16) | C2 | semidirect |
| 6. #22558163 | C2 | semidirect |
| 7. C67×D4⋊C16 | C2 | semidirect |
| 18. C4⋊(C67⋊C16) | C22 | semidirect |
| 23. C4×C67⋊C16 | C22 | semidirect |
| 25. C4⋊C16×C67 | C22 | semidirect |
| 26. C4×C16×C67 | C22 | semidirect |
| 181. D4⋊C16 | D67 | semidirect |
| 182. C67 | #11631 | semidirect |
| 196. C4⋊C16 | C2×D67 | semidirect |
| 201. C4×C16 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D4×D67 | 2 |
| #22562011 | 2 |
| #22562006 | 2 |
| #22558165 | 2 |
| D4⋊(C67⋊C16) | 2 |
| #22558163 | 2 |
| C67×D4⋊C16 | 2 |
| #11631 | 67 |