Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 3. #20266101 | C2 | direct (N × H) |
| 12. #15692194 | C4 | semidirect |
| 14. C2×#13108049 | C4 | semidirect |
| 15. C2×C16×C101 | C4 | semidirect |
| 28. #13108049 | C2×C4 | semidirect |
| 30. C16×C101 | C2×C4 | semidirect |
| 54. C2×C101 | #365 | semidirect |
| 59. C101 | C2×#365 | semidirect |
| 70. C2×C16 | #87938 | semidirect |
| 89. C16 | C2×#87938 | semidirect |
| 115. C2 | #20266101 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15692325 | 2 |
| C2×#15692323 | 2 |
| #20266101 | 2 |
| C2×#15692194 | 2 |
| C2×#365 | 101 |