Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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. C4×#13108058 | C2 | semidirect |
| 4. #20264945 | C2 | semidirect |
| 5. C4×M16×C101 | C2 | semidirect |
| 15. #15692171 | C4 | direct (N × H) |
| 32. #13108058 | C2×C4 | semidirect |
| 42. M16×C101 | C2×C4 | semidirect |
| 85. C4×C101 | #100 | semidirect |
| 96. C101 | C4×#100 | semidirect |
| 100. C4×M16 | D101 | semidirect |
| 133. M16 | C4×D101 | semidirect |
| 182. C4 | #15692171 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D404 | 2 |
| C2×#15692171 | 2 |
| C4×#13108058 | 2 |
| #20264945 | 2 |
| C4×M16×C101 | 2 |
| C4×#100 | 101 |