Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
270 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 79 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×#16839597 | C2 | semidirect |
| 2. #21448069 | C2 | semidirect |
| 3. C4×#14519683 | C2 | semidirect |
| 4. C61×#2246 | C2 | semidirect |
| 19. #14519683 | D4 | semidirect |
| 62. C4×C61 | D32 | semidirect |
| 67. #2246 | D61 | semidirect |
| 82. C61 | #13725 | semidirect |
| 130. C4 | #16839597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839597 | 2 |
| #21448069 | 2 |
| C4×#14519683 | 2 |
| C61×#2246 | 2 |
| #13725 | 61 |