Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
410 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 10. #16863801 | C4 | semidirect |
| 11. #16863747 | C4 | semidirect |
| 162. C67 | #9288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571362 | 2 |
| #22569149 | 2 |
| #22561182 | 2 |
| #22558889 | 2 |
| #22558774 | 2 |
| #22558068 | 2 |
| C67×#1275 | 2 |
| #9288 | 67 |