Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
190 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 78 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. #21460985 | C2 | semidirect |
| 4. #21460984 | C2 | semidirect |
| 14. #16839596 | C4 | semidirect |
| 16. C32×D61 | C4 | semidirect |
| 17. C61×M64 | C4 | semidirect |
| 31. #14519683 | C2×C4 | semidirect |
| 33. C32×C61 | C2×C4 | semidirect |
| 85. D61 | #1426 | semidirect |
| 91. M64 | #6923 | semidirect |
| 98. C61 | C2×#1426 | semidirect |
| 114. C32 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#368 | 2 |
| C2×#16840689 | 2 |
| #21460985 | 2 |
| #21460984 | 2 |
| M64×D61 | 2 |
| C2×#1426 | 61 |