Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
234 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21445436 | C2 | semidirect |
| 4. #21443888 | C2 | semidirect |
| 5. #21443874 | C2 | semidirect |
| 6. #21443873 | C2 | semidirect |
| 49. D8×C61 | Q16 | semidirect |
| 129. C61 | #12445 | semidirect |
| 158. D8 | #11758202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447956 | 2 |
| #21445436 | 2 |
| D8×#92418 | 2 |
| #21443888 | 2 |
| #21443874 | 2 |
| #21443873 | 2 |
| C61×#2224 | 2 |
| #12445 | 61 |