Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
202 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 9. #87839 | C4 | direct (N × H) |
| 26. C4×C52 | Q16 | semidirect |
| 65. C52 | C4×Q16 | semidirect |
| 111. C4 | #87839 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87839 | 2 |
| C4×#6039 | 2 |
| C4×#6034 | 2 |
| #11716801 | 2 |
| #11716798 | 2 |
| C4×Q16 | 25 |