Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 88. C67⋊C8 | #108 | semidirect |
| 112. C67 | #8828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22560380 | 2 |
| #22560346 | 2 |
| #22558968 | 2 |
| #22558967 | 2 |
| #22558964 | 2 |
| C2×#16863118 | 2 |
| C67×#1566 | 2 |
| #8828 | 67 |