Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×Dic194 | C2 | semidirect |
| 2. #20261068 | C2 | semidirect |
| 4. #20261039 | C2 | semidirect |
| 5. #20260954 | C2 | semidirect |
| 6. #20260890 | C2 | semidirect |
| 8. #20260840 | C2 | semidirect |
| 9. #20260835 | C2 | semidirect |
| 10. #20260792 | C2 | semidirect |
| 132. C97 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic194 | 2 |
| #20261068 | 2 |
| #20261051 | 2 |
| #20261039 | 2 |
| #20260954 | 2 |
| #20260890 | 2 |
| #20260873 | 2 |
| #20260840 | 2 |
| #20260835 | 2 |
| #20260792 | 2 |
| #529×C97 | 2 |
| #3117 | 97 |