Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
360 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 84 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. #11716897 | C2 | semidirect |
| 4. C4⋊#6034 | C2 | semidirect |
| 37. C4×C52 | M16 | semidirect |
| 40. #1039 | M16 | semidirect |
| 91. C52 | #423 | semidirect |
| 103. C4×C5 | #704 | semidirect |
| 144. C5 | #65758 | semidirect |
| 155. C4 | #87867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87867 | 2 |
| C2×C4×#1039 | 2 |
| #11716897 | 2 |
| C4⋊#6034 | 2 |
| #65758 | 5 |