Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
334 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21443799 | C2 | semidirect |
| 5. Q8⋊#11758185 | C2 | semidirect |
| 6. #21443797 | C2 | semidirect |
| 7. C61×Q8⋊C16 | C2 | semidirect |
| 152. Q8⋊C16 | D61 | semidirect |
| 176. C61 | #11639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Q8×D61 | 2 |
| #21447621 | 2 |
| #21447616 | 2 |
| #21443799 | 2 |
| Q8⋊#11758185 | 2 |
| #21443797 | 2 |
| C61×Q8⋊C16 | 2 |
| #11639 | 61 |