Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #21446735 | C2 | semidirect |
| 5. #21443914 | C2 | semidirect |
| 6. #21443909 | C2 | semidirect |
| 7. C61×#2141 | C2 | semidirect |
| 12. C2×#14519720 | C4 | semidirect |
| 42. C2×#11758185 | C2×C4 | semidirect |
| 56. C2×Q16×C61 | C2×C4 | semidirect |
| 159. #2141 | D61 | semidirect |
| 186. C61 | #13019 | semidirect |
| 194. C2×Q16 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519720 | 2 |
| #21454670 | 2 |
| C2×#16839576 | 2 |
| #21446735 | 2 |
| #21443914 | 2 |
| #21443909 | 2 |
| C61×#2141 | 2 |
| #13019 | 61 |