Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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×#16863812 | C2 | semidirect |
| 2. #22569853 | C2 | semidirect |
| 3. #22562309 | C2 | semidirect |
| 4. #22562292 | C2 | semidirect |
| 5. #22561993 | C2 | semidirect |
| 6. #22561925 | C2 | semidirect |
| 7. C22×D16×C67 | C2 | semidirect |
| 12. C2×#14523982 | C22 | semidirect |
| 13. C2×C16×D67 | C22 | semidirect |
| 15. #16863629 | C22 | semidirect |
| 18. #16863224 | C22 | semidirect |
| 19. #16863222 | C22 | semidirect |
| 20. #16863197 | C22 | semidirect |
| 52. C2×C16×C67 | D4 | semidirect |
| 130. C22×D16 | D67 | semidirect |
| 137. C67 | #33607 | semidirect |
| 179. C2×C16 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863812 | 2 |
| #22569853 | 2 |
| #22562309 | 2 |
| #22562292 | 2 |
| #22561993 | 2 |
| #22561925 | 2 |
| C22×D16×C67 | 2 |
| #33607 | 67 |