Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
822 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 147 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. #21448884 | C2 | semidirect |
| 3. #21446745 | C2 | semidirect |
| 4. #21443658 | C2 | semidirect |
| 5. C2×C61×#331 | C2 | semidirect |
| 10. #16840138 | C4 | semidirect |
| 29. #14519774 | C2×C4 | semidirect |
| 40. C4×#92418 | C2×C4 | semidirect |
| 91. C4⋊Dic61 | D8 | semidirect |
| 166. C2×#331 | D61 | semidirect |
| 189. C61 | #9061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840138 | 2 |
| #21448884 | 2 |
| #21446745 | 2 |
| #21443658 | 2 |
| C2×C61×#331 | 2 |
| #9061 | 61 |