Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
668 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 135 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. #22573346 | C2 | semidirect |
| 2. #22572008 | C2 | semidirect |
| 3. #22562326 | C2 | semidirect |
| 4. #22562282 | C2 | semidirect |
| 5. #22562165 | C2 | semidirect |
| 6. #22562091 | C2 | semidirect |
| 7. #22562047 | C2 | semidirect |
| 8. C67×#2246 | C2 | semidirect |
| 10. #16864197 | C22 | semidirect |
| 11. #16863832 | C22 | semidirect |
| 16. #16863812 | C22 | semidirect |
| 18. #16863663 | C22 | semidirect |
| 21. #16863514 | C22 | semidirect |
| 22. #16863226 | C22 | semidirect |
| 23. #16863217 | C22 | semidirect |
| 24. #16863209 | C22 | semidirect |
| 25. #16863204 | C22 | semidirect |
| 26. #16863179 | C22 | semidirect |
| 27. C2×D16×C67 | C22 | semidirect |
| 28. C2×D16×C67 | C22 | semidirect |
| 29. #493×C67 | C22 | semidirect |
| 30. C4×C16×C67 | C22 | semidirect |
| 44. Dic536 | D4 | semidirect |
| 45. #14523988 | D4 | semidirect |
| 47. D1072 | D4 | semidirect |
| 145. #2246 | D67 | semidirect |
| 151. C67 | #33858 | semidirect |
| 159. C2×D16 | C2×D67 | semidirect |
| 160. C2×D16 | C2×D67 | semidirect |
| 162. #493 | 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 |
|---|---|
| #22573346 | 2 |
| #22572008 | 2 |
| #22562326 | 2 |
| #22562282 | 2 |
| #22562165 | 2 |
| #22562091 | 2 |
| #22562047 | 2 |
| C67×#2246 | 2 |
| #33858 | 67 |