Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
183 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 85 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×#87716 | C2 | semidirect |
| 3. C22⋊#6014 | C2 | semidirect |
| 4. C4⋊#6014 | C2 | semidirect |
| 5. C4×#6014 | C2 | semidirect |
| 26. #6014 | D4 | semidirect |
| 38. C4×C25 | M16 | semidirect |
| 71. C25 | #436 | semidirect |
| 112. C4 | #87716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C25 | 2 |
| C2×#87716 | 2 |
| C22⋊#6014 | 2 |
| C4⋊#6014 | 2 |
| C4×#6014 | 2 |
| #65301 | 5 |