Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
760 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 283 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 |
|---|---|---|
| 2. C2×#87804 | C2 | semidirect |
| 3. C22⋊#6029 | C2 | semidirect |
| 11. C2×#6029 | C22 | semidirect |
| 33. C22×C52 | M16 | semidirect |
| 66. C52 | #407 | semidirect |
| 71. C22×C5 | #681 | semidirect |
| 101. C5 | #65496 | semidirect |
| 106. C22 | #87804 | 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×#87804 | 2 |
| C22⋊#6029 | 2 |
| #65496 | 5 |