Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
7134 conjugacy classes of subgroups; only the 1771 normal subgroups are shown.
This group has 7134 conjugacy classes of subgroups — too many to draw. Only its 1771 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. C23×#11758194 | C2 | semidirect |
| 2. C22×#14519694 | C2 | direct (N × H) |
| 5. C22×#11758194 | C22 | semidirect |
| 7. C2×#14519694 | C22 | direct (N × H) |
| 15. C2×#11758194 | C23 | semidirect |
| 17. #14519694 | C23 | direct (N × H) |
| 56. #11758194 | C24 | semidirect |
| 65. C23×C61 | #100 | semidirect |
| 86. C22×C61 | C2×#100 | semidirect |
| 98. C2×C61 | C22×#100 | semidirect |
| 110. C61 | C23×#100 | semidirect |
| 162. C23 | #14519694 | direct (N × H) |
| 182. C22 | C2×#14519694 | direct (N × H) |
| 191. C2 | C22×#14519694 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11758194 | 2 |
| C22×#14519694 | 2 |
| C24×D4×C61 | 2 |
| C23×#100 | 61 |