Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
296 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 71 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. #11716783 | C2 | semidirect |
| 72. C52 | #424 | semidirect |
| 110. C5 | #65696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6034 | 2 |
| C2×#87860 | 2 |
| #11717075 | 2 |
| #11716783 | 2 |
| #65696 | 5 |