Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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×#15692285 | C2 | semidirect |
| 2. C2×#15692285 | C2 | semidirect |
| 3. #20265944 | C2 | semidirect |
| 4. #20265450 | C2 | semidirect |
| 5. #20265438 | C2 | semidirect |
| 6. #20265225 | C2 | semidirect |
| 7. #20265161 | C2 | semidirect |
| 8. C2×#15692173 | C2 | semidirect |
| 16. C2×#13108064 | C22 | semidirect |
| 18. C2×#13108062 | C22 | semidirect |
| 25. #15692190 | C22 | semidirect |
| 26. #15692174 | C22 | semidirect |
| 27. #15692173 | C22 | semidirect |
| 28. #15692172 | C22 | semidirect |
| 143. C101 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692285 | 2 |
| #20265944 | 2 |
| #20265450 | 2 |
| #20265438 | 2 |
| #20265225 | 2 |
| #20265161 | 2 |
| C2×#15692173 | 2 |
| #575×C101 | 2 |
| #3069 | 101 |