Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#16863229 | C2 | semidirect |
| 2. #22562297 | C2 | semidirect |
| 4. #22558409 | C2 | semidirect |
| 5. #22558390 | C2 | semidirect |
| 6. #22558387 | C2 | semidirect |
| 7. C2×SD64×C67 | C2 | semidirect |
| 39. C32×C67 | D4 | semidirect |
| 96. C2×SD64 | D67 | semidirect |
| 103. C67 | #13699 | semidirect |
| 135. C32 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863229 | 2 |
| #22562297 | 2 |
| #22562292 | 2 |
| #22558409 | 2 |
| #22558390 | 2 |
| #22558387 | 2 |
| C2×SD64×C67 | 2 |
| #13699 | 67 |