Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
570 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #22558894 | C2 | semidirect |
| 4. #22558112 | C2 | semidirect |
| 140. C67 | #9403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569250 | 2 |
| #22560201 | 2 |
| #22558894 | 2 |
| #22558112 | 2 |
| C67×#2542 | 2 |
| #9403 | 67 |