Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
174 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 174 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 |
|---|---|---|
| 7. #16863230 | C4 | semidirect |
| 9. C2×C67⋊C32 | C4 | semidirect |
| 79. C67 | #7469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863230 | 2 |
| C67×#2108 | 2 |
| #7469 | 67 |