Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
480 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 197 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. #20260841 | C2 | direct (N × H) |
| 8. C2×Dic388 | C4 | semidirect |
| 27. Dic388 | C2×C4 | semidirect |
| 65. C2×C97 | #441 | semidirect |
| 69. C97 | C2×#441 | semidirect |
| 134. C2 | #20260841 | 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×#15690775 | 2 |
| #20260841 | 2 |
| C2×#15690733 | 2 |
| C2×#15690720 | 2 |
| C2×#106×C97 | 2 |
| C2×#441 | 97 |