Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
678 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21457126 | C2 | semidirect |
| 2. #21456737 | C2 | semidirect |
| 3. #21446747 | C2 | semidirect |
| 4. #21446738 | C2 | semidirect |
| 5. #21444314 | C2 | semidirect |
| 6. #21443670 | C2 | semidirect |
| 7. C61×#3151 | C2 | semidirect |
| 114. M16×C61 | D8 | semidirect |
| 215. #3151 | D61 | semidirect |
| 251. C61 | #10192 | semidirect |
| 337. M16 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457126 | 2 |
| #21456737 | 2 |
| #21446747 | 2 |
| #21446738 | 2 |
| #21444314 | 2 |
| #21443670 | 2 |
| C61×#3151 | 2 |
| #10192 | 61 |