Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
336 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 4. #11716778 | C2 | semidirect |
| 5. #11716777 | C2 | semidirect |
| 7. #87867 | C4 | semidirect |
| 9. C2×#6033 | C4 | semidirect |
| 78. C52 | #405 | semidirect |
| 118. C5 | #65691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87867 | 2 |
| C22×#6033 | 2 |
| #11717075 | 2 |
| #11716778 | 2 |
| #11716777 | 2 |
| #65691 | 5 |