Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21447620 | C2 | semidirect |
| 3. #21444573 | C2 | semidirect |
| 4. #21443787 | C2 | semidirect |
| 5. #21443786 | C2 | semidirect |
| 6. #21443785 | C2 | semidirect |
| 7. C61×#1333 | C2 | semidirect |
| 21. #16839538 | C22 | semidirect |
| 22. #16839513 | C22 | semidirect |
| 25. C61×#346 | C22 | semidirect |
| 26. C61×#334 | C22 | semidirect |
| 78. D8×C61 | M16 | semidirect |
| 98. D488 | M16 | semidirect |
| 167. #1333 | D61 | semidirect |
| 189. #346 | C2×D61 | semidirect |
| 192. #334 | C2×D61 | semidirect |
| 193. C61 | #11663 | semidirect |
| 248. D8 | #11758189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×D61 | 2 |
| #21447620 | 2 |
| #21444573 | 2 |
| #21443787 | 2 |
| #21443786 | 2 |
| #21443785 | 2 |
| C61×#1333 | 2 |
| #11663 | 61 |