Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1380 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1380 conjugacy classes of subgroups — too many to draw. Only its 195 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. C23×D536 | C2 | semidirect |
| 2. C2×#16863834 | C2 | semidirect |
| 3. #22569790 | C2 | semidirect |
| 4. #22562140 | C2 | semidirect |
| 5. #22562123 | C2 | semidirect |
| 6. #22561926 | C2 | semidirect |
| 7. C67×#2112 | C2 | semidirect |
| 9. C2×#14524065 | C22 | semidirect |
| 17. C2×#14523988 | C22 | semidirect |
| 18. C2×D1072 | C22 | semidirect |
| 19. #16863637 | C22 | semidirect |
| 20. #16863632 | C22 | semidirect |
| 22. #16863434 | C22 | semidirect |
| 24. #16863198 | C22 | semidirect |
| 26. C2×M32×C67 | C22 | semidirect |
| 27. C22⋊C16×C67 | C22 | semidirect |
| 37. C2×Dic268 | C23 | semidirect |
| 45. C2×D536 | D4 | semidirect |
| 47. C2×D536 | C23 | semidirect |
| 56. #14523977 | C23 | semidirect |
| 67. C2×C16×C67 | C23 | semidirect |
| 158. C22×C67 | #509 | semidirect |
| 185. #2112 | D67 | semidirect |
| 186. C67 | #33517 | semidirect |
| 199. C2×M32 | C2×D67 | semidirect |
| 206. C22⋊C16 | C2×D67 | semidirect |
| 242. C2×C16 | C22×D67 | semidirect |
| 343. C22 | #16863834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D536 | 2 |
| C2×#16863834 | 2 |
| #22569790 | 2 |
| #22562140 | 2 |
| #22562123 | 2 |
| #22561926 | 2 |
| C67×#2112 | 2 |
| #33517 | 67 |