Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
296 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 13. #15692184 | C4 | semidirect |
| 15. C8×Dic101 | C4 | semidirect |
| 30. #13108053 | C8 | direct (N × H) |
| 63. C8×C101 | C4⋊C4 | semidirect |
| 78. Dic101 | C4×C8 | semidirect |
| 85. C101 | C8×C4⋊C4 | semidirect |
| 150. C8 | #13108053 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692184 | 2 |
| C2×C8×Dic101 | 2 |
| C4×#13108053 | 2 |
| #20264932 | 2 |
| #20264931 | 2 |
| C2×C4×C8×C101 | 2 |
| C8×C4⋊C4 | 101 |