Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
232 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 59 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×#16839597 | C2 | semidirect |
| 2. #21448067 | C2 | semidirect |
| 3. D16×Dic61 | C2 | semidirect |
| 4. #21444014 | C2 | semidirect |
| 5. #21443998 | C2 | semidirect |
| 6. #21443997 | C2 | semidirect |
| 7. C2×C61×D32 | C2 | semidirect |
| 38. D16×C61 | D4 | semidirect |
| 96. Dic61 | D32 | semidirect |
| 98. C2×D32 | D61 | semidirect |
| 123. C61 | #13685 | semidirect |
| 136. D16 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839597 | 2 |
| #21448067 | 2 |
| D16×Dic61 | 2 |
| #21444014 | 2 |
| #21443998 | 2 |
| #21443997 | 2 |
| C2×C61×D32 | 2 |
| #13685 | 61 |