Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 3. #20261017 | C2 | semidirect |
| 4. #20260942 | C2 | semidirect |
| 6. #20260840 | C2 | semidirect |
| 104. C97 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic194 | 2 |
| #20261063 | 2 |
| #20261017 | 2 |
| #20260942 | 2 |
| #20260890 | 2 |
| #20260840 | 2 |
| #20260792 | 2 |
| #533×C97 | 2 |
| #3113 | 97 |