Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 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×#16864387 | C2 | semidirect |
| 2. #22575427 | C2 | semidirect |
| 3. #22575374 | C2 | semidirect |
| 4. C22⋊#14524130 | C2 | semidirect |
| 5. C22×D4×C269 | C2 | semidirect |
| 6. C2×D1076 | C22 | semidirect |
| 9. C2×#14524130 | C22 | semidirect |
| 10. C4⋊Dic269 | C22 | semidirect |
| 29. D4×C269 | D4 | semidirect |
| 39. C22×C269 | D8 | semidirect |
| 53. C269 | #447 | semidirect |
| 55. C22×D4 | D269 | semidirect |
| 81. D4 | C22⋊D269 | semidirect |
| 96. C22 | #16864387 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16864387 | 2 |
| #22575427 | 2 |
| #22575374 | 2 |
| C22⋊#14524130 | 2 |
| C22×D4×C269 | 2 |
| #447 | 269 |