Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
712 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16840053 | C2 | semidirect |
| 3. #21446620 | C2 | semidirect |
| 4. C2×#16839489 | C2 | semidirect |
| 5. C61×#1296 | C2 | semidirect |
| 27. #14519777 | D4 | semidirect |
| 48. C4⋊C8×C61 | D4 | semidirect |
| 157. #1296 | D61 | semidirect |
| 178. C61 | #10235 | semidirect |
| 203. C4⋊C8 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840053 | 2 |
| #21450735 | 2 |
| #21446620 | 2 |
| C2×#16839489 | 2 |
| C61×#1296 | 2 |
| #10235 | 61 |