Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
190 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 58 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×#16864412 | C2 | semidirect |
| 2. #22575510 | C2 | semidirect |
| 3. C22⋊#14524137 | C2 | semidirect |
| 6. C2×#14524137 | C22 | semidirect |
| 34. C22×C269 | M16 | semidirect |
| 42. C2×D269 | M16 | semidirect |
| 53. C269 | #407 | semidirect |
| 95. C22 | #16864412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864412 | 2 |
| #22575510 | 2 |
| C22⋊#14524137 | 2 |
| C22×C4×D269 | 2 |
| #407 | 269 |