Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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. #21448092 | C2 | semidirect |
| 4. #21443875 | C2 | semidirect |
| 5. Q8⋊#11758185 | C2 | semidirect |
| 7. C61×#1674 | C2 | semidirect |
| 79. D488 | Q16 | semidirect |
| 126. #1674 | D61 | semidirect |
| 151. C61 | #12404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D488 | 2 |
| #21448092 | 2 |
| #21447953 | 2 |
| #21443875 | 2 |
| Q8⋊#11758185 | 2 |
| #21443779 | 2 |
| C61×#1674 | 2 |
| #12404 | 61 |