Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 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. #22570868 | C2 | semidirect |
| 3. #22562429 | C2 | semidirect |
| 4. #22562386 | C2 | semidirect |
| 5. #22562291 | C2 | semidirect |
| 7. #22562102 | C2 | semidirect |
| 8. C67×#2166 | C2 | semidirect |
| 13. #16863798 | C22 | semidirect |
| 14. #16863776 | C22 | semidirect |
| 22. #16863504 | C22 | semidirect |
| 26. #16863219 | C22 | semidirect |
| 27. #16863213 | C22 | semidirect |
| 30. #364×C67 | C22 | semidirect |
| 32. #347×C67 | C22 | semidirect |
| 168. #2166 | D67 | semidirect |
| 169. C67 | #33693 | semidirect |
| 189. #364 | C2×D67 | semidirect |
| 193. #347 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570868 | 2 |
| #22569113 | 2 |
| #22562429 | 2 |
| #22562386 | 2 |
| #22562291 | 2 |
| #22562162 | 2 |
| #22562102 | 2 |
| C67×#2166 | 2 |
| #33693 | 67 |