Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
534 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16840197 | C2 | semidirect |
| 2. #21455535 | C2 | semidirect |
| 3. C2×#16840033 | C2 | semidirect |
| 4. C2×#16839576 | C2 | semidirect |
| 5. #21447439 | C2 | semidirect |
| 6. #21443932 | C2 | semidirect |
| 7. C61×#2143 | C2 | semidirect |
| 207. #2143 | D61 | semidirect |
| 240. C61 | #13323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840197 | 2 |
| #21455535 | 2 |
| C2×#16840033 | 2 |
| C2×#16839576 | 2 |
| #21447439 | 2 |
| #21443932 | 2 |
| C61×#2143 | 2 |
| #13323 | 61 |