Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
232 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 9. #15692325 | C4 | semidirect |
| 12. C8×#87938 | C4 | semidirect |
| 15. #15692188 | C4 | semidirect |
| 16. #15692187 | C4 | semidirect |
| 17. #106×C101 | C4 | semidirect |
| 69. C101 | #1772 | semidirect |
| 83. #106 | #87938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692325 | 2 |
| #20266142 | 2 |
| C2×C8×#87938 | 2 |
| #20266047 | 2 |
| #20265212 | 2 |
| #1772 | 101 |