Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
202 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. #22562067 | C2 | semidirect |
| 4. #22558389 | C2 | semidirect |
| 6. C32×Dic67 | C2 | semidirect |
| 7. C67×#1424 | C2 | semidirect |
| 12. #16863235 | C4 | semidirect |
| 25. Dic536 | C2×C4 | semidirect |
| 36. C32×C67 | C2×C4 | semidirect |
| 80. Dic67 | SD64 | semidirect |
| 89. #1424 | D67 | semidirect |
| 93. C67 | C4×SD64 | semidirect |
| 122. C32 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863235 | 2 |
| #22562067 | 2 |
| #22562055 | 2 |
| #22558389 | 2 |
| #22558386 | 2 |
| C32×Dic67 | 2 |
| C67×#1424 | 2 |
| C4×SD64 | 67 |