Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
226 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #22558274 | C2 | semidirect |
| 35. C67⋊C16 | M16 | semidirect |
| 87. C67 | #12019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863172 | 2 |
| #22558965 | 2 |
| #22558274 | 2 |
| C67×#1568 | 2 |
| #12019 | 67 |