Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21450825 | C2 | semidirect |
| 4. #21443697 | C2 | semidirect |
| 5. #21443686 | C2 | semidirect |
| 6. #21443667 | C2 | semidirect |
| 52. C22×D4×C61 | Q8 | semidirect |
| 59. C2×C4⋊C4×C61 | Q8 | semidirect |
| 256. C61 | #10374 | semidirect |
| 259. C22×D4 | Dic122 | semidirect |
| 277. C2×C4⋊C4 | Dic122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21450825 | 2 |
| #21444387 | 2 |
| C2×#16839496 | 2 |
| #21443697 | 2 |
| #21443686 | 2 |
| #21443667 | 2 |
| C61×#1964 | 2 |
| #10374 | 61 |