Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
172 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 33 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. C2×#87775 | C2 | semidirect |
| 3. C2×#87765 | C2 | semidirect |
| 4. #11716793 | C2 | direct (N × H) |
| 9. #87775 | C22 | semidirect |
| 12. #87765 | C22 | semidirect |
| 44. C2×C52 | SD32 | semidirect |
| 72. C52 | C2×SD32 | semidirect |
| 123. C2 | #11716793 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87775 | 2 |
| C2×#87770 | 2 |
| C2×#87765 | 2 |
| #11716793 | 2 |
| C2×SD32 | 25 |