Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
636 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 143 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. #22573359 | C2 | semidirect |
| 2. #22572014 | C2 | semidirect |
| 3. #22562462 | C2 | semidirect |
| 4. #22562335 | C2 | semidirect |
| 5. #22562290 | C2 | semidirect |
| 6. #22562188 | C2 | semidirect |
| 7. #22562047 | C2 | semidirect |
| 8. C67×#2178 | C2 | semidirect |
| 145. #2178 | D67 | semidirect |
| 147. C67 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573359 | 2 |
| #22572014 | 2 |
| #22562462 | 2 |
| #22562335 | 2 |
| #22562290 | 2 |
| #22562188 | 2 |
| #22562047 | 2 |
| C67×#2178 | 2 |
| #33860 | 67 |