Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
189 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 189 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #11716363 | C2 | semidirect |
| 36. Dic25 | M16 | semidirect |
| 64. C25 | #423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×C25 | 2 |
| C2×C4×Dic25 | 2 |
| C2×#87716 | 2 |
| #11716363 | 2 |
| #65407 | 5 |