Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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. C25×C22⋊Q8 | C2 | semidirect |
| 3. C2×#87724 | C2 | semidirect |
| 4. C2×#87723 | C2 | semidirect |
| 5. C22⋊#6014 | C2 | semidirect |
| 6. #11716358 | C2 | semidirect |
| 7. #11716357 | C2 | semidirect |
| 106. C22⋊Q8 | D25 | semidirect |
| 110. C25 | #452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87744 | 2 |
| C25×C22⋊Q8 | 2 |
| C2×#87724 | 2 |
| C2×#87723 | 2 |
| C22⋊#6014 | 2 |
| #11716358 | 2 |
| #11716357 | 2 |
| #65336 | 5 |