Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22575448 | C2 | semidirect |
| 2. #22575444 | C2 | semidirect |
| 3. #22575442 | C2 | semidirect |
| 4. #22575438 | C2 | semidirect |
| 5. #22575429 | C2 | semidirect |
| 7. C4×D1076 | C2 | semidirect |
| 8. C4×D1076 | C2 | semidirect |
| 9. #22575410 | C2 | semidirect |
| 10. C42×D269 | C2 | semidirect |
| 11. C4×Q8×C269 | C2 | semidirect |
| 74. C269 | #529 | semidirect |
| 82. C4×Q8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575448 | 2 |
| #22575444 | 2 |
| #22575442 | 2 |
| #22575438 | 2 |
| #22575429 | 2 |
| #22575428 | 2 |
| C4×D1076 | 2 |
| #22575410 | 2 |
| C42×D269 | 2 |
| C4×Q8×C269 | 2 |
| #529 | 269 |