Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 118 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. #20261601 | C2 | semidirect |
| 26. C22×C4×C97 | C8 | semidirect |
| 69. C97 | #1817 | semidirect |
| 91. C22×C4 | #11715897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11715897 | 2 |
| #20261601 | 2 |
| C22×C4×Dic97 | 2 |
| #1817 | 97 |