Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1124 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 195 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. C23×Dic244 | C2 | semidirect |
| 2. C2×#16840205 | C2 | semidirect |
| 4. #21447755 | C2 | semidirect |
| 5. #21447738 | C2 | semidirect |
| 6. #21447540 | C2 | semidirect |
| 7. C61×#2112 | C2 | semidirect |
| 17. C2×Dic488 | C22 | semidirect |
| 18. C2×#14519722 | C22 | semidirect |
| 24. #16839567 | C22 | semidirect |
| 43. C2×Dic244 | D4 | semidirect |
| 154. C22×C61 | #510 | semidirect |
| 171. #2112 | D61 | semidirect |
| 197. C61 | #33518 | semidirect |
| 325. C22 | #16840205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic244 | 2 |
| C2×#16840205 | 2 |
| #21455400 | 2 |
| #21447755 | 2 |
| #21447738 | 2 |
| #21447540 | 2 |
| C61×#2112 | 2 |
| #33518 | 61 |