Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 3. Q16×#92418 | C2 | semidirect |
| 4. #21443882 | C2 | semidirect |
| 5. #21443877 | C2 | semidirect |
| 7. C61×#2227 | C2 | semidirect |
| 51. Q16×C61 | SD16 | semidirect |
| 105. #2227 | D61 | semidirect |
| 131. C61 | #12419 | semidirect |
| 160. Q16 | #11758201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447859 | 2 |
| #21445412 | 2 |
| Q16×#92418 | 2 |
| #21443882 | 2 |
| #21443877 | 2 |
| #21443866 | 2 |
| C61×#2227 | 2 |
| #12419 | 61 |