Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
294 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 59 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. #21458955 | C2 | semidirect |
| 2. #21448132 | C2 | semidirect |
| 3. #21444005 | C2 | semidirect |
| 4. #21443959 | C2 | semidirect |
| 5. C61×#2218 | C2 | semidirect |
| 13. #16839596 | C22 | semidirect |
| 14. C2×D16×C61 | C22 | semidirect |
| 17. C61×#367 | C22 | semidirect |
| 28. Dic488 | D4 | semidirect |
| 32. D976 | D4 | semidirect |
| 109. #2218 | D61 | semidirect |
| 122. C2×D16 | C2×D61 | semidirect |
| 128. #367 | C2×D61 | semidirect |
| 130. C61 | #13667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458955 | 2 |
| #21448132 | 2 |
| #21444005 | 2 |
| #21443959 | 2 |
| C61×#2218 | 2 |
| #13667 | 61 |