Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
570 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22558894 | C2 | semidirect |
| 5. #22558111 | C2 | semidirect |
| 6. #22558110 | C2 | semidirect |
| 7. C67×#1549 | C2 | semidirect |
| 177. #1549 | D67 | semidirect |
| 180. C67 | #9403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569249 | 2 |
| #22565163 | 2 |
| #22560198 | 2 |
| #22558894 | 2 |
| #22558111 | 2 |
| #22558110 | 2 |
| C67×#1549 | 2 |
| #9403 | 67 |