Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
706 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #21443648 | C2 | semidirect |
| 4. #21443647 | C2 | semidirect |
| 5. C61×#1274 | C2 | semidirect |
| 11. #16839813 | C4 | semidirect |
| 14. C4×#11758189 | C4 | semidirect |
| 40. C4×#92418 | C2×C4 | semidirect |
| 47. C4×C8×C61 | C2×C4 | semidirect |
| 69. C42×C61 | M16 | semidirect |
| 82. C4×Dic61 | M16 | semidirect |
| 137. #1274 | D61 | semidirect |
| 157. C61 | #7855 | semidirect |
| 182. C4×C8 | C4×D61 | semidirect |
| 218. C42 | #11758189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454447 | 2 |
| #376×D61 | 2 |
| #21443648 | 2 |
| #21443647 | 2 |
| C61×#1274 | 2 |
| #7855 | 61 |