Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
460 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#16863219 | C2 | semidirect |
| 5. #22560962 | C2 | semidirect |
| 6. #22558315 | C2 | semidirect |
| 7. C67×#1375 | C2 | semidirect |
| 19. #16863198 | C4 | semidirect |
| 40. #14523977 | C2×C4 | semidirect |
| 54. C2×C16×C67 | C2×C4 | semidirect |
| 151. #1375 | D67 | semidirect |
| 152. C67 | #12956 | semidirect |
| 191. C2×C16 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863509 | 2 |
| C2×#16863219 | 2 |
| C2×#16863210 | 2 |
| #22561926 | 2 |
| #22560962 | 2 |
| #22558315 | 2 |
| C67×#1375 | 2 |
| #12956 | 67 |