Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20265204 | C2 | semidirect |
| 5. C2×C4×#11717579 | C2 | semidirect |
| 6. #20264941 | C2 | semidirect |
| 7. #339×C101 | C2 | semidirect |
| 14. #15692178 | C4 | semidirect |
| 15. #15692175 | C4 | semidirect |
| 91. C101 | #1937 | semidirect |
| 98. #339 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265204 | 2 |
| C2×#15692183 | 2 |
| #20265171 | 2 |
| #20265145 | 2 |
| C2×C4×#11717579 | 2 |
| #20264941 | 2 |
| #339×C101 | 2 |
| #1937 | 101 |