Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 100 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. #11716895 | C2 | semidirect |
| 4. C4×#6034 | C2 | semidirect |
| 8. #87867 | C4 | direct (N × H) |
| 25. #6034 | C2×C4 | semidirect |
| 36. C4×C52 | M16 | semidirect |
| 39. #1039 | M16 | semidirect |
| 87. C52 | C4×M16 | semidirect |
| 99. C4×C5 | #704 | semidirect |
| 137. C5 | C4×#704 | semidirect |
| 147. C4 | #87867 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87867 | 2 |
| C2×C4×#1039 | 2 |
| #11716895 | 2 |
| C4×#6034 | 2 |
| C4×#704 | 5 |