Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
298 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 298 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 |
|---|---|---|
| 1. C2×#16863233 | C2 | semidirect |
| 2. C2×#16863231 | C2 | semidirect |
| 3. #22562295 | C2 | semidirect |
| 4. #22558390 | C2 | semidirect |
| 5. #22558387 | C2 | semidirect |
| 6. C22⋊(C67⋊C32) | C2 | semidirect |
| 7. C2×#508×C67 | C2 | semidirect |
| 39. Q32×C67 | D4 | semidirect |
| 42. D16×C67 | D4 | semidirect |
| 115. C2×#508 | D67 | semidirect |
| 122. C67 | #13663 | semidirect |
| 148. Q32 | C22⋊D67 | semidirect |
| 153. D16 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863233 | 2 |
| C2×#16863231 | 2 |
| #22562295 | 2 |
| #22558390 | 2 |
| #22558387 | 2 |
| C22⋊(C67⋊C32) | 2 |
| C2×#508×C67 | 2 |
| #13663 | 67 |