Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 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×#15692198 | C2 | semidirect |
| 3. #20265447 | C2 | semidirect |
| 4. #20264993 | C2 | semidirect |
| 5. #20264984 | C2 | semidirect |
| 6. #20264961 | C2 | semidirect |
| 7. #578×C101 | C2 | semidirect |
| 91. C101 | #2193 | semidirect |
| 92. #578 | D101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20265612 | 2 |
| C2×#15692198 | 2 |
| #20265447 | 2 |
| #20264993 | 2 |
| #20264984 | 2 |
| #20264961 | 2 |
| #578×C101 | 2 |
| #2193 | 101 |