Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
326 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 89 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. C2×#15692254 | C2 | semidirect |
| 4. #20264940 | C2 | semidirect |
| 5. #20264939 | C2 | semidirect |
| 6. #20264931 | C2 | semidirect |
| 48. C2×D4×C101 | Q8 | semidirect |
| 124. C101 | #2023 | semidirect |
| 156. C2×D4 | Dic202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692254 | 2 |
| C2×#15692176 | 2 |
| #20265080 | 2 |
| #20264940 | 2 |
| #20264939 | 2 |
| #20264931 | 2 |
| C2×#102×C101 | 2 |
| #2023 | 101 |