Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21455535 | C2 | semidirect |
| 2. C2×#16840029 | C2 | semidirect |
| 3. C2×#16839575 | C2 | semidirect |
| 4. #21447547 | C2 | semidirect |
| 5. #21447439 | C2 | semidirect |
| 6. #21443931 | C2 | semidirect |
| 7. C2×C61×#509 | C2 | semidirect |
| 203. C2×#509 | 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 |
|---|---|
| #21455535 | 2 |
| C2×#16840029 | 2 |
| C2×#16839575 | 2 |
| #21447547 | 2 |
| #21447439 | 2 |
| #21443931 | 2 |
| C2×C61×#509 | 2 |
| #13323 | 61 |