Finite Group DatabasebetaFinite Group DatabasebetaOrder 17216.
192 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22575451 | C2 | semidirect |
| 4. #22575444 | C2 | semidirect |
| 5. #22575444 | C2 | semidirect |
| 6. #22575443 | C2 | semidirect |
| 8. Q8×Dic269 | C2 | semidirect |
| 9. #22575418 | C2 | semidirect |
| 67. C269 | #541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22575451 | 2 |
| #22575446 | 2 |
| #22575444 | 2 |
| #22575443 | 2 |
| #22575432 | 2 |
| Q8×Dic269 | 2 |
| #22575418 | 2 |
| #22575412 | 2 |
| C22⋊Q8×C269 | 2 |
| #541 | 269 |