Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
684 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 4. #22559884 | C2 | semidirect |
| 5. #22559856 | C2 | semidirect |
| 6. #22559841 | C2 | semidirect |
| 7. #22559805 | C2 | semidirect |
| 160. C67 | #19751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570950 | 2 |
| #22570756 | 2 |
| #22570590 | 2 |
| #22559884 | 2 |
| #22559856 | 2 |
| #22559841 | 2 |
| #22559805 | 2 |
| #22558512 | 2 |
| C67×#3185 | 2 |
| #19751 | 67 |