Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
668 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 151 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. #22573350 | C2 | semidirect |
| 2. #22572009 | C2 | semidirect |
| 3. #22562459 | C2 | semidirect |
| 4. #22562329 | C2 | semidirect |
| 5. #22562286 | C2 | semidirect |
| 6. #22562168 | C2 | semidirect |
| 7. #22562091 | C2 | semidirect |
| 8. C67×#2170 | C2 | semidirect |
| 9. #16864201 | C22 | semidirect |
| 12. #16863834 | C22 | semidirect |
| 16. C2×D1072 | C22 | semidirect |
| 17. C2×D1072 | C22 | semidirect |
| 18. #16863773 | C22 | semidirect |
| 20. #16863666 | C22 | semidirect |
| 22. #16863514 | C22 | semidirect |
| 23. #16863226 | C22 | semidirect |
| 24. #16863210 | C22 | semidirect |
| 25. #16863204 | C22 | semidirect |
| 26. #504×C67 | C22 | semidirect |
| 28. #364×C67 | C22 | semidirect |
| 29. #350×C67 | C22 | semidirect |
| 30. C4×C16×C67 | C22 | semidirect |
| 45. Dic536 | D4 | semidirect |
| 47. #14523988 | D4 | semidirect |
| 52. D1072 | D4 | semidirect |
| 150. #2170 | D67 | semidirect |
| 151. C67 | #33858 | semidirect |
| 161. #504 | C2×D67 | semidirect |
| 169. #364 | C2×D67 | semidirect |
| 172. #350 | C2×D67 | semidirect |
| 173. C4×C16 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573350 | 2 |
| #22572009 | 2 |
| #22562459 | 2 |
| #22562329 | 2 |
| #22562286 | 2 |
| #22562168 | 2 |
| #22562091 | 2 |
| C67×#2170 | 2 |
| #33858 | 67 |