Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#16839595 | C2 | semidirect |
| 3. C22⋊#14519683 | C2 | semidirect |
| 4. #21443956 | C2 | semidirect |
| 5. C61×C22⋊C32 | C2 | semidirect |
| 14. C2×#14519683 | C22 | semidirect |
| 16. C2×C32×C61 | C22 | semidirect |
| 91. C22×C61 | M64 | semidirect |
| 99. C2×D61 | M64 | semidirect |
| 109. C22⋊C32 | D61 | semidirect |
| 126. C2×C32 | C2×D61 | semidirect |
| 127. C61 | #13553 | semidirect |
| 208. C22 | #16839595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D61 | 2 |
| C2×#16839595 | 2 |
| C22⋊#14519683 | 2 |
| #21443956 | 2 |
| C61×C22⋊C32 | 2 |
| #13553 | 61 |