Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #22562409 | C2 | semidirect |
| 3. #22562407 | C2 | semidirect |
| 5. #22558226 | C2 | semidirect |
| 7. C67×#1350 | C2 | semidirect |
| 156. #1350 | D67 | semidirect |
| 158. C67 | #12286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571099 | 2 |
| #22562409 | 2 |
| #22562407 | 2 |
| #22561651 | 2 |
| #22558226 | 2 |
| #22558134 | 2 |
| C67×#1350 | 2 |
| #12286 | 67 |