Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
212 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 49 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. #11716791 | C2 | direct (N × H) |
| 40. C2×C52 | #108 | semidirect |
| 64. C52 | C2×#108 | semidirect |
| 117. C2 | #11716791 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87862 | 2 |
| C2×#87769 | 2 |
| #11716791 | 2 |
| C2×#108 | 25 |