Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#16863839 | C2 | semidirect |
| 2. C22×#14523987 | C2 | semidirect |
| 4. #22569076 | C2 | semidirect |
| 5. #22562270 | C2 | semidirect |
| 6. #22562248 | C2 | semidirect |
| 7. #22561969 | C2 | semidirect |
| 8. #22561914 | C2 | semidirect |
| 9. C67×#2140 | C2 | semidirect |
| 16. C2×Dic536 | C22 | semidirect |
| 17. C2×#14523988 | C22 | semidirect |
| 25. #16863490 | C22 | semidirect |
| 28. Dic67⋊C16 | C22 | semidirect |
| 29. #16863199 | C22 | semidirect |
| 30. #16863196 | C22 | semidirect |
| 42. C2×Dic268 | D4 | semidirect |
| 184. #2140 | D67 | semidirect |
| 186. C67 | #33587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863839 | 2 |
| C22×#14523987 | 2 |
| #22570690 | 2 |
| #22569076 | 2 |
| #22562270 | 2 |
| #22562248 | 2 |
| #22561969 | 2 |
| #22561914 | 2 |
| C67×#2140 | 2 |
| #33587 | 67 |