Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22558900 | C2 | semidirect |
| 4. #22558665 | C2 | semidirect |
| 6. #22558083 | C2 | semidirect |
| 7. C67×#1567 | C2 | semidirect |
| 184. #1567 | D67 | semidirect |
| 189. C67 | #10461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570008 | 2 |
| #22560198 | 2 |
| #22558900 | 2 |
| #22558665 | 2 |
| C2×#16863125 | 2 |
| #22558083 | 2 |
| C67×#1567 | 2 |
| #10461 | 67 |