Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
512 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22570865 | C2 | semidirect |
| 3. #22562427 | C2 | semidirect |
| 4. #22562386 | C2 | semidirect |
| 5. #22562385 | C2 | semidirect |
| 6. #22562287 | C2 | semidirect |
| 8. #22562103 | C2 | semidirect |
| 9. #22562101 | C2 | semidirect |
| 10. #22562024 | C2 | semidirect |
| 11. C67×#2214 | C2 | semidirect |
| 16. #16863798 | C22 | semidirect |
| 25. #16863503 | C22 | semidirect |
| 30. #16863220 | C22 | semidirect |
| 31. #16863219 | C22 | semidirect |
| 32. #16863217 | C22 | semidirect |
| 33. #16863212 | C22 | semidirect |
| 37. #16863173 | C22 | semidirect |
| 39. #494×C67 | C22 | semidirect |
| 41. #364×C67 | C22 | semidirect |
| 42. #362×C67 | C22 | semidirect |
| 213. #2214 | D67 | semidirect |
| 218. C67 | #33693 | semidirect |
| 225. #494 | C2×D67 | semidirect |
| 243. #364 | C2×D67 | semidirect |
| 245. #362 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570865 | 2 |
| #22569107 | 2 |
| #22562427 | 2 |
| #22562386 | 2 |
| #22562385 | 2 |
| #22562287 | 2 |
| #22562158 | 2 |
| #22562103 | 2 |
| #22562101 | 2 |
| #22562024 | 2 |
| C67×#2214 | 2 |
| #33693 | 67 |