Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 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. #22575540 | C2 | direct (N × H) |
| 2. C2×#16864412 | C2 | semidirect |
| 3. C2×#16864411 | C2 | semidirect |
| 4. C2×D269⋊C8 | C2 | semidirect |
| 5. C22×#14524137 | C2 | semidirect |
| 7. #16864412 | C22 | semidirect |
| 8. #16864411 | C22 | semidirect |
| 9. D269⋊C8 | C22 | semidirect |
| 13. C2×#14524137 | C22 | semidirect |
| 46. C2×C269 | #131 | semidirect |
| 49. C269 | C2×#131 | semidirect |
| 97. C2 | #22575540 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575540 | 2 |
| C2×#16864412 | 2 |
| C2×#16864411 | 2 |
| C2×D269⋊C8 | 2 |
| C22×#14524137 | 2 |
| C2×#16864401 | 2 |
| C2×#131 | 269 |