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. #21448094 | C2 | semidirect |
| 4. #21445213 | C2 | semidirect |
| 5. #21443873 | C2 | semidirect |
| 7. C61×Q8⋊C16 | C2 | semidirect |
| 79. D488 | Q16 | semidirect |
| 128. Q8⋊C16 | 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 |
| #21448094 | 2 |
| #21447957 | 2 |
| #21445213 | 2 |
| #21443873 | 2 |
| #21443781 | 2 |
| C61×Q8⋊C16 | 2 |
| #12404 | 61 |