Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20266013 | C2 | semidirect |
| 2. C2×#15692281 | C2 | semidirect |
| 3. #20265349 | C2 | semidirect |
| 4. #20265344 | C2 | semidirect |
| 5. #20265195 | C2 | semidirect |
| 6. #20265161 | C2 | semidirect |
| 7. #535×C101 | C2 | semidirect |
| 8. #15692303 | C22 | semidirect |
| 12. #15692300 | C22 | semidirect |
| 17. #15692281 | C22 | semidirect |
| 20. C2×#13108058 | C22 | semidirect |
| 21. #15692183 | C22 | semidirect |
| 22. #15692174 | C22 | semidirect |
| 23. #15692172 | C22 | semidirect |
| 25. C22×D4×C101 | C22 | semidirect |
| 26. #127×C101 | C22 | semidirect |
| 27. #124×C101 | C22 | semidirect |
| 30. #117×C101 | C22 | semidirect |
| 37. #13108074 | D4 | semidirect |
| 42. C2×Dic202 | D4 | semidirect |
| 45. C2×D404 | D4 | semidirect |
| 135. C101 | #3021 | semidirect |
| 138. #535 | D101 | semidirect |
| 152. C22×D4 | C2×D101 | semidirect |
| 158. #127 | C2×D101 | semidirect |
| 159. #124 | C2×D101 | semidirect |
| 162. #117 | C2×D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266013 | 2 |
| C2×#15692281 | 2 |
| #20265349 | 2 |
| #20265344 | 2 |
| #20265195 | 2 |
| #20265161 | 2 |
| #535×C101 | 2 |
| #3021 | 101 |