Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
303 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 303 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#6014 | C2 | semidirect |
| 3. C22⋊#6014 | C2 | direct (N × H) |
| 11. C2×#6014 | C22 | semidirect |
| 15. C23×C25 | C8 | semidirect |
| 34. C22×C25 | C2×C8 | semidirect |
| 50. C2×C25 | C22⋊C8 | semidirect |
| 70. C25 | C2×C22⋊C8 | semidirect |
| 97. C23 | #6014 | semidirect |
| 113. C22 | C2×#6014 | semidirect |
| 121. C2 | C22⋊#6014 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C25 | 2 |
| C22×#6014 | 2 |
| C22⋊#6014 | 2 |
| C2×C22⋊#168 | 5 |