Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 171 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×#87810 | C2 | semidirect |
| 3. #11717244 | C2 | semidirect |
| 4. #11716699 | C2 | semidirect |
| 5. C22⋊#6029 | C2 | semidirect |
| 11. C2×#6045 | C22 | semidirect |
| 14. C4⋊#1039 | C22 | semidirect |
| 16. C2×#6029 | C22 | semidirect |
| 44. C22×C52 | SD16 | semidirect |
| 87. C52 | #450 | semidirect |
| 94. C22×C5 | #687 | semidirect |
| 131. C5 | #65507 | semidirect |
| 138. C22 | #87810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C2×#87810 | 2 |
| #11717244 | 2 |
| #11716699 | 2 |
| C22⋊#6029 | 2 |
| #65507 | 5 |