Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
582 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 3. #22562456 | C2 | semidirect |
| 4. #22562455 | C2 | semidirect |
| 5. #22562454 | C2 | semidirect |
| 6. #22562453 | C2 | semidirect |
| 9. C67×#2245 | C2 | semidirect |
| 145. D67 | #2245 | direct (N × H) |
| 152. #2245 | D67 | direct (N × H) |
| 155. C67 | C2×#2245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D67 | 2 |
| #494×D67 | 2 |
| #22562456 | 2 |
| #22562455 | 2 |
| #22562454 | 2 |
| #22562453 | 2 |
| #358×D67 | 2 |
| #346×D67 | 2 |
| C67×#2245 | 2 |
| C2×#2245 | 67 |