Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
284 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 284 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 |
|---|---|---|
| 2. #21448137 | C2 | semidirect |
| 3. C2×#16839599 | C2 | semidirect |
| 4. #21444008 | C2 | semidirect |
| 5. #21444002 | C2 | semidirect |
| 6. #21443961 | C2 | semidirect |
| 7. C61×#2222 | C2 | semidirect |
| 18. #16839596 | C22 | semidirect |
| 19. C2×#14519683 | C22 | semidirect |
| 20. C2×Q32×C61 | C22 | semidirect |
| 23. C61×#368 | C22 | semidirect |
| 118. #2222 | D61 | semidirect |
| 132. C2×Q32 | C2×D61 | semidirect |
| 142. #368 | C2×D61 | semidirect |
| 144. C61 | #13671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458960 | 2 |
| #21448137 | 2 |
| C2×#16839599 | 2 |
| #21444008 | 2 |
| #21444002 | 2 |
| #21443961 | 2 |
| C61×#2222 | 2 |
| #13671 | 61 |