Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
194 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 65 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×#16839602 | C2 | semidirect |
| 4. #21444018 | C2 | semidirect |
| 5. #21444000 | C2 | semidirect |
| 6. #21443999 | C2 | semidirect |
| 79. C22×C61 | Q64 | semidirect |
| 112. C61 | #13695 | semidirect |
| 170. C22 | #16839602 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839602 | 2 |
| C22×#14519683 | 2 |
| #21447910 | 2 |
| #21444018 | 2 |
| #21444000 | 2 |
| #21443999 | 2 |
| C61×#2216 | 2 |
| #13695 | 61 |