Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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. #20265225 | C2 | semidirect |
| 5. #20264949 | C2 | semidirect |
| 6. #20264937 | C2 | semidirect |
| 7. C4×M16×C101 | C2 | semidirect |
| 16. #15692173 | C4 | semidirect |
| 17. #15692171 | C4 | semidirect |
| 96. C101 | #1932 | semidirect |
| 101. C4×M16 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265225 | 2 |
| #20265193 | 2 |
| C2×#15692183 | 2 |
| #20265159 | 2 |
| #20264949 | 2 |
| #20264937 | 2 |
| C4×M16×C101 | 2 |
| #1932 | 101 |