Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#15690802 | C2 | semidirect |
| 2. #20261042 | C2 | semidirect |
| 3. #20261035 | C2 | semidirect |
| 4. #20260778 | C2 | semidirect |
| 5. #20260759 | C2 | semidirect |
| 91. C97 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690802 | 2 |
| #20261042 | 2 |
| #20261035 | 2 |
| #20260778 | 2 |
| #20260759 | 2 |
| #20260736 | 2 |
| C4×#41×C97 | 2 |
| #3080 | 97 |