Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
374 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22558984 | C2 | semidirect |
| 4. #22558981 | C2 | semidirect |
| 6. #22558106 | C2 | semidirect |
| 7. C67×#1301 | C2 | semidirect |
| 168. #1301 | D67 | semidirect |
| 169. C67 | #8863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568846 | 2 |
| #22560190 | 2 |
| #22558984 | 2 |
| #22558981 | 2 |
| #22558521 | 2 |
| #22558106 | 2 |
| C67×#1301 | 2 |
| #8863 | 67 |