Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
314 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 2. #20260865 | C2 | semidirect |
| 3. #20260864 | C2 | semidirect |
| 4. #20260863 | C2 | semidirect |
| 5. #20260862 | C2 | semidirect |
| 92. C97 | #2987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261288 | 2 |
| #20260865 | 2 |
| #20260864 | 2 |
| #20260863 | 2 |
| #20260862 | 2 |
| #20260796 | 2 |
| #20260793 | 2 |
| #20260789 | 2 |
| #433×C97 | 2 |
| #2987 | 97 |