Finite Group DatabasebetaFinite Group DatabasebetaOrder 12928.
400 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 160 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. #20266201 | C2 | semidirect |
| 2. #20266194 | C2 | semidirect |
| 3. #20266193 | C2 | semidirect |
| 4. #20266184 | C2 | semidirect |
| 6. C4×#13108084 | C2 | semidirect |
| 7. C4×D101⋊C8 | C2 | semidirect |
| 105. C101 | #2922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20266201 | 2 |
| #20266194 | 2 |
| #20266193 | 2 |
| #20266184 | 2 |
| #20266151 | 2 |
| C4×#13108084 | 2 |
| C4×D101⋊C8 | 2 |
| C4×#13108073 | 2 |
| #2922 | 101 |