Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
200 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. Q32×Dic67 | C2 | semidirect |
| 3. #22558409 | C2 | semidirect |
| 4. #22558390 | C2 | semidirect |
| 6. #22558342 | C2 | semidirect |
| 18. SD64×C67 | C4 | semidirect |
| 32. Q32×C67 | C2×C4 | semidirect |
| 36. C32×C67 | C2×C4 | semidirect |
| 93. C67 | #13652 | semidirect |
| 98. SD64 | Dic67 | semidirect |
| 111. Q32 | C2×Dic67 | semidirect |
| 122. C32 | C2×Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×Dic67 | 2 |
| D16×Dic67 | 2 |
| #22558409 | 2 |
| #22558390 | 2 |
| #22558387 | 2 |
| #22558342 | 2 |
| C2×SD64×C67 | 2 |
| #13652 | 67 |