Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
218 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 42. Q16×C67 | Q16 | semidirect |
| 88. C67 | #12446 | semidirect |
| 122. Q16 | Dic268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562351 | 2 |
| #22559827 | 2 |
| #22558279 | 2 |
| #22558265 | 2 |
| C8×Q16×C67 | 2 |
| #12446 | 67 |