Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1380 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 211 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×#16863832 | C2 | semidirect |
| 2. #22569790 | C2 | semidirect |
| 3. #22562138 | C2 | semidirect |
| 4. #22562121 | C2 | semidirect |
| 5. #22561925 | C2 | semidirect |
| 6. #22561820 | C2 | semidirect |
| 7. C23×D8×C67 | C2 | semidirect |
| 8. C2×#14524065 | C22 | semidirect |
| 11. C2×#14523987 | C22 | semidirect |
| 12. C2×#14523984 | C22 | semidirect |
| 13. C2×#14523983 | C22 | semidirect |
| 14. #16863637 | C22 | semidirect |
| 15. #16863632 | C22 | semidirect |
| 17. #16863434 | C22 | semidirect |
| 19. #16863197 | C22 | semidirect |
| 20. C22⋊(C67⋊C16) | C22 | semidirect |
| 30. C2×Dic268 | C23 | semidirect |
| 32. C2×D536 | C23 | semidirect |
| 42. C2×C67⋊C16 | C23 | semidirect |
| 43. #14523977 | C23 | semidirect |
| 61. C2×D8×C67 | D4 | semidirect |
| 162. C22×C67 | #509 | semidirect |
| 179. C23×D8 | D67 | semidirect |
| 186. C67 | #33517 | semidirect |
| 226. C2×D8 | C22⋊D67 | semidirect |
| 343. C22 | #16863832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863832 | 2 |
| #22569790 | 2 |
| #22562138 | 2 |
| #22562121 | 2 |
| #22561925 | 2 |
| #22561820 | 2 |
| C23×D8×C67 | 2 |
| #33517 | 67 |