Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C2×C4⋊Dic269 | C2 | semidirect |
| 3. C2×C22⋊Dic269 | C2 | semidirect |
| 4. C2×#16864379 | C2 | semidirect |
| 5. C2×#16864379 | C2 | semidirect |
| 6. #22575360 | C2 | semidirect |
| 7. C2×C22⋊C4×C269 | C2 | semidirect |
| 53. C2×C4×C269 | D4 | semidirect |
| 89. C269 | #394 | semidirect |
| 96. C2×C22⋊C4 | D269 | semidirect |
| 143. C2×C4 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D269 | 2 |
| C2×C4⋊Dic269 | 2 |
| C2×C22⋊Dic269 | 2 |
| C2×#16864379 | 2 |
| #22575360 | 2 |
| C2×C22⋊C4×C269 | 2 |
| #394 | 269 |