Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
222 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 71 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×#87723 | C2 | semidirect |
| 4. #11716384 | C2 | semidirect |
| 38. C22×C25 | Q16 | semidirect |
| 79. C25 | #451 | semidirect |
| 120. C22 | #87723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×C25 | 2 |
| C2×#87723 | 2 |
| #11716486 | 2 |
| #11716384 | 2 |
| C22⋊#6014 | 2 |
| #65517 | 5 |