Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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. #22573347 | C2 | semidirect |
| 2. #22572009 | C2 | semidirect |
| 3. #22562459 | C2 | semidirect |
| 4. #22562330 | C2 | semidirect |
| 5. #22562285 | C2 | semidirect |
| 6. #22562167 | C2 | semidirect |
| 7. #22562047 | C2 | semidirect |
| 8. C67×#2178 | C2 | semidirect |
| 10. #16864198 | C22 | semidirect |
| 12. #16863831 | C22 | semidirect |
| 14. C2×D1072 | C22 | semidirect |
| 15. C2×D1072 | C22 | semidirect |
| 17. #16863812 | C22 | semidirect |
| 18. #16863773 | C22 | semidirect |
| 19. #16863667 | C22 | semidirect |
| 23. #16863217 | C22 | semidirect |
| 24. #16863208 | C22 | semidirect |
| 25. #16863179 | C22 | semidirect |
| 27. #443×C67 | C22 | semidirect |
| 28. #368×C67 | C22 | semidirect |
| 29. #359×C67 | C22 | semidirect |
| 30. C4×C16×C67 | C22 | semidirect |
| 58. Q32×C67 | D4 | semidirect |
| 59. SD32×C67 | D4 | semidirect |
| 60. D16×C67 | D4 | semidirect |
| 149. #2178 | D67 | semidirect |
| 151. C67 | #33858 | semidirect |
| 167. #443 | C2×D67 | semidirect |
| 168. #368 | C2×D67 | semidirect |
| 171. #359 | C2×D67 | semidirect |
| 173. C4×C16 | C2×D67 | semidirect |
| 190. Q32 | D268 | semidirect |
| 192. SD32 | D268 | semidirect |
| 197. D16 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573347 | 2 |
| #22572009 | 2 |
| #22562459 | 2 |
| #22562330 | 2 |
| #22562285 | 2 |
| #22562167 | 2 |
| #22562047 | 2 |
| C67×#2178 | 2 |
| #33858 | 67 |