Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
548 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. #21461698 | C2 | semidirect |
| 2. C8×C22⋊#6923 | C2 | semidirect |
| 3. #21461216 | C2 | semidirect |
| 4. #21461215 | C2 | semidirect |
| 5. #21461096 | C2 | semidirect |
| 6. #21461094 | C2 | semidirect |
| 20. C22×#11758199 | C4 | semidirect |
| 28. C2×#14519710 | C4 | semidirect |
| 29. C2×#14519699 | C4 | semidirect |
| 30. C2×#102×C61 | C4 | semidirect |
| 243. C2×#102 | #6923 | semidirect |
| 255. C61 | #9815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461698 | 2 |
| C8×C22⋊#6923 | 2 |
| #21461216 | 2 |
| #21461215 | 2 |
| #21461096 | 2 |
| #21461094 | 2 |
| C2×#16839997 | 2 |
| #9815 | 61 |