Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21443889 | C2 | semidirect |
| 4. #21443874 | C2 | semidirect |
| 5. C61×#1713 | C2 | semidirect |
| 51. D488 | Q16 | semidirect |
| 86. #1713 | D61 | semidirect |
| 105. C61 | #12445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447953 | 2 |
| C8×D488 | 2 |
| #21443889 | 2 |
| #21443874 | 2 |
| C61×#1713 | 2 |
| #12445 | 61 |