Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
7646 conjugacy classes of subgroups; only the 1976 normal subgroups are shown.
This group has 7646 conjugacy classes of subgroups — too many to draw. Only its 1976 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. C24×#92420 | C2 | semidirect |
| 2. C22×#14519834 | C2 | direct (N × H) |
| 5. C23×#92420 | C22 | semidirect |
| 6. C2×#14519834 | C22 | direct (N × H) |
| 14. C22×#92420 | C23 | semidirect |
| 15. #14519834 | C23 | direct (N × H) |
| 18. C24×D61 | C8 | semidirect |
| 37. C23×D61 | C2×C8 | semidirect |
| 50. C2×#92420 | C24 | semidirect |
| 51. C23×C61 | C22⋊C8 | semidirect |
| 59. C22×D61 | C22×C8 | semidirect |
| 71. C22×C61 | C2×C22⋊C8 | semidirect |
| 79. C2×D61 | C23×C8 | semidirect |
| 86. C2×C61 | C22×C22⋊C8 | semidirect |
| 100. C61 | C23×C22⋊C8 | semidirect |
| 144. C23 | #14519834 | direct (N × H) |
| 162. C22 | C2×#14519834 | direct (N × H) |
| 171. C2 | C22×#14519834 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#92420 | 2 |
| C22×#14519834 | 2 |
| C24×C4×D61 | 2 |
| C23×C22⋊C8 | 61 |