Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
302 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16839596 | C2 | semidirect |
| 2. C2×#16839588 | C2 | semidirect |
| 3. #21444000 | C2 | semidirect |
| 4. #21443997 | C2 | semidirect |
| 13. C61×#508 | C4 | semidirect |
| 30. Q32×C61 | C2×C4 | semidirect |
| 33. D16×C61 | C2×C4 | semidirect |
| 103. #508 | Dic61 | semidirect |
| 113. C61 | #13616 | semidirect |
| 123. Q32 | C2×Dic61 | semidirect |
| 126. D16 | C2×Dic61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839596 | 2 |
| C2×#16839588 | 2 |
| #21444000 | 2 |
| #21443997 | 2 |
| C2×C61×#508 | 2 |
| #13616 | 61 |