Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
188 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 188 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 |
|---|---|---|
| 12. Q64×C67 | C4 | semidirect |
| 60. C67 | #13653 | semidirect |
| 63. Q64 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×Dic67 | 2 |
| #22558411 | 2 |
| #22558390 | 2 |
| #22558342 | 2 |
| C2×Q64×C67 | 2 |
| #13653 | 67 |