Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. C22×Dic388 | C2 | semidirect |
| 3. C2×#15690728 | C2 | semidirect |
| 5. #341×C97 | C2 | semidirect |
| 80. C97 | #2020 | semidirect |
| 85. #341 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690843 | 2 |
| C22×Dic388 | 2 |
| C2×#15690728 | 2 |
| #20260701 | 2 |
| #341×C97 | 2 |
| #2020 | 97 |