Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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×#16864391 | C2 | semidirect |
| 2. C2×#16864390 | C2 | semidirect |
| 3. C2×#16864387 | C2 | semidirect |
| 4. #22575449 | C2 | semidirect |
| 5. #22575440 | C2 | semidirect |
| 6. #22575363 | C2 | semidirect |
| 7. C2×D8×C269 | C2 | semidirect |
| 29. #14524130 | D4 | semidirect |
| 37. C8×C269 | D4 | semidirect |
| 54. C269 | #496 | semidirect |
| 59. C2×D8 | D269 | semidirect |
| 92. C8 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864391 | 2 |
| C2×#16864390 | 2 |
| C2×#16864387 | 2 |
| #22575449 | 2 |
| #22575440 | 2 |
| #22575363 | 2 |
| C2×D8×C269 | 2 |
| #496 | 269 |