Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 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 |
|---|---|---|
| 1. #20261340 | C2 | semidirect |
| 2. #20261036 | C2 | semidirect |
| 3. #20260988 | C2 | semidirect |
| 4. #20260971 | C2 | semidirect |
| 5. #20260931 | C2 | semidirect |
| 6. #424×C97 | C2 | semidirect |
| 72. C97 | #3259 | semidirect |
| 78. #424 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261340 | 2 |
| #20261036 | 2 |
| #20260988 | 2 |
| #20260971 | 2 |
| #20260931 | 2 |
| #424×C97 | 2 |
| #3259 | 97 |