Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
1784 conjugacy classes of subgroups; only the 379 normal subgroups are shown.
This group has 1784 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. #13107005 | C2 | semidirect |
| 2. C4×C52×M16 | C2 | semidirect |
| 3. #13102997 | C2 | semidirect |
| 4. #13102575 | C2 | semidirect |
| 5. #13102558 | C2 | semidirect |
| 6. #13102557 | C2 | semidirect |
| 7. #13102543 | C2 | semidirect |
| 46. C4×C5×M16 | D5 | semidirect |
| 68. C52×C8 | #41 | semidirect |
| 123. C4×M16 | C5⋊D5 | semidirect |
| 144. C5×C8 | #709 | semidirect |
| 161. C52 | #3184 | semidirect |
| 213. C8 | #87900 | semidirect |
| 214. C5 | #10610266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13107005 | 2 |
| C4×C52×M16 | 2 |
| #13102997 | 2 |
| #13102575 | 2 |
| #13102558 | 2 |
| #13102557 | 2 |
| #13102543 | 2 |
| #10610266 | 5 |