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. #22570869 | C2 | semidirect |
| 3. #22562430 | C2 | semidirect |
| 4. #22562382 | C2 | semidirect |
| 5. #22562291 | C2 | semidirect |
| 6. #22562290 | C2 | semidirect |
| 8. #22562099 | C2 | semidirect |
| 9. #22562097 | C2 | semidirect |
| 10. #22562024 | C2 | semidirect |
| 11. C67×#2231 | C2 | semidirect |
| 17. #16863776 | C22 | semidirect |
| 26. #16863502 | C22 | semidirect |
| 31. #16863218 | C22 | semidirect |
| 32. #16863217 | C22 | semidirect |
| 33. #16863213 | C22 | semidirect |
| 34. #16863211 | C22 | semidirect |
| 37. #16863173 | C22 | semidirect |
| 38. #499×C67 | C22 | semidirect |
| 40. #365×C67 | C22 | semidirect |
| 41. #364×C67 | C22 | semidirect |
| 211. #2231 | D67 | semidirect |
| 218. C67 | #33693 | semidirect |
| 224. #499 | C2×D67 | semidirect |
| 241. #365 | C2×D67 | semidirect |
| 243. #364 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570869 | 2 |
| #22569107 | 2 |
| #22562430 | 2 |
| #22562382 | 2 |
| #22562291 | 2 |
| #22562290 | 2 |
| #22562161 | 2 |
| #22562099 | 2 |
| #22562097 | 2 |
| #22562024 | 2 |
| C67×#2231 | 2 |
| #33693 | 67 |