Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
202 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. C2×#16839595 | C2 | semidirect |
| 3. C4⋊#14519683 | C2 | semidirect |
| 4. #21443956 | C2 | semidirect |
| 5. C4×C32×C61 | C2 | semidirect |
| 27. C32×C61 | D4 | semidirect |
| 60. C4×C61 | M64 | semidirect |
| 68. C4×C32 | D61 | semidirect |
| 82. C61 | #13646 | semidirect |
| 95. C32 | D244 | semidirect |
| 128. C4 | #16839595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839595 | 2 |
| C16×D244 | 2 |
| C4⋊#14519683 | 2 |
| #21443956 | 2 |
| C4×C32×C61 | 2 |
| #13646 | 61 |