Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
300 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. #20266143 | C2 | semidirect |
| 4. C4×D101⋊C8 | C2 | semidirect |
| 5. #20266052 | C2 | semidirect |
| 6. #20266048 | C2 | semidirect |
| 8. #15692343 | C4 | semidirect |
| 10. #15692342 | C4 | semidirect |
| 17. #15692318 | C4 | semidirect |
| 18. #15692317 | C4 | semidirect |
| 25. #15692183 | C4 | semidirect |
| 26. #15692182 | C4 | semidirect |
| 27. #15692181 | C4 | semidirect |
| 28. #104×C101 | C4 | semidirect |
| 121. C101 | #1764 | semidirect |
| 144. #104 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D101⋊#131 | 2 |
| #20266167 | 2 |
| #20266143 | 2 |
| C4×D101⋊C8 | 2 |
| #20266052 | 2 |
| #20266048 | 2 |
| #104×D101 | 2 |
| #1764 | 101 |