Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
204 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 204 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×#16839599 | C2 | semidirect |
| 2. C22×#14519683 | C2 | semidirect |
| 4. #21444020 | C2 | semidirect |
| 5. #21444000 | C2 | semidirect |
| 6. #21443996 | C2 | semidirect |
| 7. C61×#2216 | C2 | semidirect |
| 28. #14519683 | D4 | semidirect |
| 80. C22×C61 | SD64 | semidirect |
| 93. #2216 | D61 | semidirect |
| 116. C61 | #13696 | semidirect |
| 178. C22 | #16839599 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839599 | 2 |
| C22×#14519683 | 2 |
| #21447905 | 2 |
| #21444020 | 2 |
| #21444000 | 2 |
| #21443996 | 2 |
| C61×#2216 | 2 |
| #13696 | 61 |