Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
346 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. #22571611 | C2 | semidirect |
| 3. #22561493 | C2 | semidirect |
| 4. #22558203 | C2 | semidirect |
| 5. #22558201 | C2 | semidirect |
| 6. #22558159 | C2 | semidirect |
| 7. C67×#2191 | C2 | semidirect |
| 172. #2191 | D67 | semidirect |
| 178. C67 | #12175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571611 | 2 |
| #22562155 | 2 |
| #22561493 | 2 |
| #22558203 | 2 |
| #22558201 | 2 |
| #22558159 | 2 |
| C67×#2191 | 2 |
| #12175 | 67 |