Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
242 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 242 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 |
|---|---|---|
| 4. #11716783 | C2 | semidirect |
| 5. #11716783 | C2 | semidirect |
| 6. #11716778 | C2 | semidirect |
| 7. #11716777 | C2 | semidirect |
| 130. C52 | #433 | semidirect |
| 197. C5 | #65697 | semidirect |
| 198. C5 | #65697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717075 | 2 |
| C22⋊#6034 | 2 |
| C22⋊#6033 | 2 |
| #11716783 | 2 |
| #11716778 | 2 |
| #11716777 | 2 |
| #65697 | 5 |