Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
282 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 282 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 |
|---|---|---|
| 56. Dic268 | Q16 | semidirect |
| 125. C67 | #12406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic268 | 2 |
| #22562489 | 2 |
| #22562348 | 2 |
| #22558268 | 2 |
| Q8⋊(C67⋊C16) | 2 |
| #22558172 | 2 |
| C67×#1674 | 2 |
| #12406 | 67 |