Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16840178 | C2 | semidirect |
| 3. #21447554 | C2 | semidirect |
| 4. C2×#16839570 | C2 | semidirect |
| 5. #21445870 | C2 | semidirect |
| 6. #21443932 | C2 | semidirect |
| 7. C61×#1382 | C2 | semidirect |
| 16. #16840038 | C4 | semidirect |
| 17. #16840033 | C4 | semidirect |
| 181. #1382 | D61 | semidirect |
| 209. C61 | #13071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840178 | 2 |
| #21455540 | 2 |
| #21447554 | 2 |
| C2×#16839570 | 2 |
| #21445870 | 2 |
| #21443932 | 2 |
| C61×#1382 | 2 |
| #13071 | 61 |