Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1390 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1390 conjugacy classes of subgroups — too many to draw. Only its 280 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. C22×#14519852 | C2 | semidirect |
| 2. C22×#14519847 | C2 | semidirect |
| 3. C2×#16840680 | C2 | direct (N × H) |
| 7. C2×#14519852 | C22 | semidirect |
| 10. C2×#14519847 | C22 | semidirect |
| 11. #16840680 | C22 | direct (N × H) |
| 25. #14519852 | C23 | semidirect |
| 28. #14519847 | C23 | semidirect |
| 132. C22×C61 | #361 | semidirect |
| 151. C2×C61 | C2×#361 | semidirect |
| 172. C61 | C22×#361 | semidirect |
| 291. C22 | #16840680 | direct (N × H) |
| 301. C2 | C2×#16840680 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519852 | 2 |
| C22×#14519847 | 2 |
| C2×#16840680 | 2 |
| C22×D8×D61 | 2 |
| C22×#361 | 61 |