Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
512 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22570863 | C2 | semidirect |
| 3. #22562428 | C2 | semidirect |
| 4. #22562384 | C2 | semidirect |
| 5. #22562289 | C2 | semidirect |
| 8. #22562103 | C2 | semidirect |
| 9. #22562099 | C2 | semidirect |
| 10. #22562022 | C2 | semidirect |
| 11. C67×#2239 | C2 | semidirect |
| 17. #16863796 | C22 | semidirect |
| 18. #16863774 | C22 | semidirect |
| 26. #16863503 | C22 | semidirect |
| 27. #16863502 | C22 | semidirect |
| 31. #16863220 | C22 | semidirect |
| 32. #16863216 | C22 | semidirect |
| 33. #16863211 | C22 | semidirect |
| 37. #16863173 | C22 | semidirect |
| 40. #365×C67 | C22 | semidirect |
| 41. #362×C67 | C22 | semidirect |
| 201. #2239 | D67 | semidirect |
| 209. C67 | #33693 | semidirect |
| 232. #365 | C2×D67 | semidirect |
| 235. #362 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570863 | 2 |
| #22569111 | 2 |
| #22562428 | 2 |
| #22562384 | 2 |
| #22562289 | 2 |
| #22562162 | 2 |
| #22562159 | 2 |
| #22562103 | 2 |
| #22562099 | 2 |
| #22562022 | 2 |
| C67×#2239 | 2 |
| #33693 | 67 |