Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
278 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22558310 | C2 | semidirect |
| 5. #22558306 | C2 | semidirect |
| 6. #22558298 | C2 | semidirect |
| 7. C67×#1833 | C2 | semidirect |
| 140. #1833 | D67 | semidirect |
| 144. C67 | #13489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561956 | 2 |
| #22561914 | 2 |
| #22561107 | 2 |
| #22558310 | 2 |
| #22558306 | 2 |
| #22558298 | 2 |
| C67×#1833 | 2 |
| #13489 | 67 |