Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
474 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22560392 | C2 | semidirect |
| 4. #22558729 | C2 | semidirect |
| 6. #22558085 | C2 | semidirect |
| 7. C67×#1901 | C2 | semidirect |
| 223. #1901 | D67 | semidirect |
| 229. C67 | #10558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570962 | 2 |
| #22560672 | 2 |
| #22560392 | 2 |
| #22558729 | 2 |
| #22558726 | 2 |
| #22558085 | 2 |
| C67×#1901 | 2 |
| #10558 | 67 |