Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
216 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21447657 | C2 | semidirect |
| 3. #21443894 | C2 | semidirect |
| 4. #21443792 | C2 | semidirect |
| 5. #21443791 | C2 | semidirect |
| 6. C16×#92418 | C2 | semidirect |
| 7. C61×#2170 | C2 | semidirect |
| 25. #14519723 | C8 | semidirect |
| 26. #14519721 | C8 | semidirect |
| 27. #14519720 | C8 | semidirect |
| 28. #14519718 | C8 | semidirect |
| 101. #2170 | D61 | semidirect |
| 125. C61 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447698 | 2 |
| #21447657 | 2 |
| #21443894 | 2 |
| #21443792 | 2 |
| #21443791 | 2 |
| C16×#92418 | 2 |
| C61×#2170 | 2 |
| #12046 | 61 |