Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
144 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 3. #11716384 | C2 | semidirect |
| 4. #11716384 | C2 | semidirect |
| 6. #11716356 | C2 | semidirect |
| 7. #11716355 | C2 | semidirect |
| 87. C25 | #485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C22⋊Q8 | 2 |
| #11716488 | 2 |
| #11716384 | 2 |
| C22⋊#6014 | 2 |
| #11716356 | 2 |
| #11716355 | 2 |
| #65334 | 5 |