Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1830 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 1830 conjugacy classes of subgroups — too many to draw. Only its 667 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 |
|---|---|---|
| 1. #22566174 | C2 | direct (N × H) |
| 92. C2×C67 | #2645 | semidirect |
| 102. C67 | C2×#2645 | semidirect |
| 187. C2 | #22566174 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22566174 | 2 |
| C2×C67⋊#401 | 2 |
| C2×#16863337 | 2 |
| C2×#16863302 | 2 |
| C2×#16863294 | 2 |
| C2×#376×C67 | 2 |
| C2×#2645 | 67 |