Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #21447607 | C2 | semidirect |
| 4. #21446605 | C2 | semidirect |
| 5. #21443916 | C2 | semidirect |
| 6. #21443909 | C2 | semidirect |
| 25. C61×#361 | C4 | semidirect |
| 59. M32×C61 | C2×C4 | semidirect |
| 62. #108×C61 | C2×C4 | semidirect |
| 182. #361 | Dic61 | semidirect |
| 185. C61 | #12940 | semidirect |
| 205. M32 | C2×Dic61 | semidirect |
| 211. #108 | C2×Dic61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454671 | 2 |
| #21447607 | 2 |
| C2×#16839563 | 2 |
| #21446605 | 2 |
| #21443916 | 2 |
| #21443909 | 2 |
| C2×C61×#361 | 2 |
| #12940 | 61 |