Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
780 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16840152 | C2 | semidirect |
| 2. #21446642 | C2 | semidirect |
| 3. C2×#16839502 | C2 | semidirect |
| 4. #21443700 | C2 | semidirect |
| 5. C61×#2819 | C2 | semidirect |
| 30. #14519774 | D4 | semidirect |
| 34. #14519688 | D4 | semidirect |
| 141. #2819 | D61 | semidirect |
| 165. C61 | #10078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840152 | 2 |
| #21446642 | 2 |
| C2×#16839502 | 2 |
| #21443700 | 2 |
| C61×#2819 | 2 |
| #10078 | 61 |