Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
486 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 80 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. #13098718 | C2 | semidirect |
| 5. #13097887 | C2 | semidirect |
| 17. C25×#100 | C4 | semidirect |
| 18. #11716380 | C4 | semidirect |
| 19. #11716372 | C4 | semidirect |
| 40. M16×C25 | C2×C4 | semidirect |
| 41. #87716 | C2×C4 | semidirect |
| 180. #100 | #1035 | semidirect |
| 181. C25 | #1856 | semidirect |
| 213. M16 | C2×#1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13099670 | 2 |
| #13098769 | 2 |
| #13098718 | 2 |
| #100×D25 | 2 |
| #13097887 | 2 |
| #10603925 | 5 |