Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
186 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 52 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. C2×#16864411 | C2 | semidirect |
| 2. #22575513 | C2 | direct (N × H) |
| 5. #16864411 | C22 | semidirect |
| 47. C2×C269 | #100 | semidirect |
| 50. C269 | C2×#100 | semidirect |
| 99. C2 | #22575513 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864411 | 2 |
| #22575513 | 2 |
| C22×C22⋊D269 | 2 |
| C2×#100 | 269 |