Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
504 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 199 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. #11716681 | C2 | semidirect |
| 36. #1039 | M16 | semidirect |
| 64. C52 | #423 | semidirect |
| 95. C5 | #65407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×M16 | 2 |
| C2×C4×#1039 | 2 |
| C2×#87804 | 2 |
| #11716681 | 2 |
| #65407 | 5 |