Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #20261043 | C2 | semidirect |
| 5. #20260946 | C2 | semidirect |
| 7. #20260843 | C2 | semidirect |
| 8. C4×Dic388 | C2 | semidirect |
| 96. C97 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261347 | 2 |
| #20261212 | 2 |
| #20261077 | 2 |
| #20261043 | 2 |
| #20260946 | 2 |
| #20260893 | 2 |
| #20260843 | 2 |
| C4×Dic388 | 2 |
| #433×C97 | 2 |
| #3127 | 97 |