Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
552 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 102. M16×C67 | Q16 | semidirect |
| 167. C67 | #10155 | semidirect |
| 247. M16 | #11761618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571157 | 2 |
| #22570755 | 2 |
| C2×#16863775 | 2 |
| #22558895 | 2 |
| #22558663 | 2 |
| #22558047 | 2 |
| C67×#1997 | 2 |
| #10155 | 67 |