Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
936 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 291 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. C2×#87806 | C2 | semidirect |
| 5. #11716698 | C2 | semidirect |
| 14. C22⋊#1039 | C4 | semidirect |
| 33. C2×#1039 | C2×C4 | semidirect |
| 43. C22×C52 | C4⋊C4 | semidirect |
| 92. C52 | #385 | semidirect |
| 97. C22×C5 | #683 | semidirect |
| 140. C5 | #65499 | semidirect |
| 145. C22 | #87806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C52 | 2 |
| C2×C22⋊#1039 | 2 |
| C2×#87806 | 2 |
| #11716698 | 2 |
| #65499 | 5 |