Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1600 conjugacy classes of subgroups; only the 379 normal subgroups are shown.
This group has 1600 conjugacy classes of subgroups — too many to draw. Only its 379 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 |
|---|---|---|
| 1. C2×#11717224 | C2 | semidirect |
| 2. C22×#87801 | C2 | semidirect |
| 3. C2×C52×M32 | C2 | semidirect |
| 4. #13102771 | C2 | direct (N × H) |
| 5. C2×#11716666 | C2 | semidirect |
| 6. C2×#11716667 | C2 | semidirect |
| 10. C2×#87802 | C22 | semidirect |
| 12. #11717224 | C22 | semidirect |
| 16. C2×#87801 | C22 | semidirect |
| 17. C2×#87801 | C22 | semidirect |
| 19. C52×M32 | C22 | semidirect |
| 20. C2×C52×C16 | C22 | semidirect |
| 21. #11716667 | C22 | semidirect |
| 22. #11716666 | C22 | semidirect |
| 41. #87802 | C23 | semidirect |
| 46. #87801 | C23 | semidirect |
| 48. C52×C16 | C23 | semidirect |
| 51. C2×C5×M32 | D5 | semidirect |
| 89. C5×M32 | C2×D5 | semidirect |
| 90. C2×C5×C16 | C2×D5 | semidirect |
| 130. C5×C16 | C22×D5 | semidirect |
| 136. C2×M32 | C5⋊D5 | semidirect |
| 138. C2×C52 | #509 | semidirect |
| 178. M32 | C2×C5⋊D5 | semidirect |
| 179. C2×C16 | C2×C5⋊D5 | semidirect |
| 180. C52 | C2×#509 | semidirect |
| 217. C16 | C22×C5⋊D5 | semidirect |
| 219. C2×C5 | #65197 | semidirect |
| 245. C5 | C2×#65197 | semidirect |
| 261. C2 | #13102771 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11717224 | 2 |
| C22×#87801 | 2 |
| C2×C52×M32 | 2 |
| #13102771 | 2 |
| C2×#11716666 | 2 |
| C2×#11716667 | 2 |
| C2×#65197 | 5 |