Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20265612 | C2 | semidirect |
| 2. C2×#15692196 | C2 | semidirect |
| 3. #20265447 | C2 | semidirect |
| 4. #20264990 | C2 | semidirect |
| 5. #20264984 | C2 | semidirect |
| 6. #20264961 | C2 | semidirect |
| 7. #576×C101 | C2 | semidirect |
| 9. C2×D808 | C22 | semidirect |
| 13. #15692195 | C22 | semidirect |
| 14. C2×#13108049 | C22 | semidirect |
| 15. #15692191 | C22 | semidirect |
| 94. C101 | #2192 | semidirect |
| 95. #576 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265612 | 2 |
| C2×#15692196 | 2 |
| #20265447 | 2 |
| #20264990 | 2 |
| #20264984 | 2 |
| #20264961 | 2 |
| #576×C101 | 2 |
| #2192 | 101 |