Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20260540 | C2 | direct (N × H) |
| 8. C2×Dic388 | C4 | semidirect |
| 24. Dic388 | C2×C4 | semidirect |
| 57. C2×C97 | #358 | semidirect |
| 62. C97 | C2×#358 | semidirect |
| 119. C2 | #20260540 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic388 | 2 |
| C2×#15690744 | 2 |
| #20260540 | 2 |
| C22×C16×C97 | 2 |
| C2×#358 | 97 |