Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
110 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 40 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 |
|---|---|---|
| 1. #20261621 | C2 | semidirect |
| 2. #20261598 | C2 | semidirect |
| 20. D8×C97 | C8 | semidirect |
| 50. C97 | #1331 | semidirect |
| 64. D8 | #11715897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261621 | 2 |
| #20261598 | 2 |
| D8×Dic97 | 2 |
| #1331 | 97 |