Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
212 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. #21443891 | C2 | semidirect |
| 5. #21443877 | C2 | semidirect |
| 6. #21443874 | C2 | semidirect |
| 7. C61×#2254 | C2 | semidirect |
| 64. C16×C61 | SD16 | semidirect |
| 99. #2254 | D61 | semidirect |
| 125. C61 | #12456 | semidirect |
| 168. C16 | #11758201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447652 | 2 |
| #21445215 | 2 |
| #21445205 | 2 |
| #21443891 | 2 |
| #21443877 | 2 |
| #21443874 | 2 |
| C61×#2254 | 2 |
| #12456 | 61 |