Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
248 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 51 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. #11716790 | C2 | semidirect |
| 30. #1044 | M16 | semidirect |
| 72. C52 | #423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1044 | 2 |
| #11716936 | 2 |
| #11716790 | 2 |
| #423 | 25 |