Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
426 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #22558111 | C2 | semidirect |
| 5. #22558110 | C2 | semidirect |
| 6. #22558067 | C2 | semidirect |
| 7. C67×#1286 | C2 | semidirect |
| 171. #1286 | D67 | semidirect |
| 172. C67 | #8771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22563184 | 2 |
| #22560198 | 2 |
| #22558529 | 2 |
| #22558111 | 2 |
| #22558110 | 2 |
| #22558067 | 2 |
| C67×#1286 | 2 |
| #8771 | 67 |