Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
536 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22570859 | C2 | semidirect |
| 2. #22569113 | C2 | semidirect |
| 3. #22562424 | C2 | semidirect |
| 4. #22562386 | C2 | semidirect |
| 5. #22562286 | C2 | semidirect |
| 6. #22562157 | C2 | semidirect |
| 7. #22562109 | C2 | semidirect |
| 8. C67×#2166 | C2 | semidirect |
| 13. #16863798 | C22 | semidirect |
| 14. #16863773 | C22 | semidirect |
| 22. #16863509 | C22 | semidirect |
| 26. #16863219 | C22 | semidirect |
| 27. #16863210 | C22 | semidirect |
| 30. #364×C67 | C22 | semidirect |
| 32. #347×C67 | C22 | semidirect |
| 174. #2166 | D67 | semidirect |
| 175. C67 | #33692 | semidirect |
| 195. #364 | C2×D67 | semidirect |
| 199. #347 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570859 | 2 |
| #22569113 | 2 |
| #22562424 | 2 |
| #22562386 | 2 |
| #22562286 | 2 |
| #22562157 | 2 |
| #22562109 | 2 |
| C67×#2166 | 2 |
| #33692 | 67 |