Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
448 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 448 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. C2×#16840659 | C2 | semidirect |
| 2. C2×#16840630 | C2 | semidirect |
| 3. #21460791 | C2 | semidirect |
| 4. #21460789 | C2 | semidirect |
| 14. #16840017 | C4 | semidirect |
| 16. #16840012 | C4 | semidirect |
| 20. #16839800 | C4 | semidirect |
| 22. C2×#135×C61 | C4 | semidirect |
| 51. #14519709 | C2×C4 | semidirect |
| 52. #14519709 | C2×C4 | semidirect |
| 60. C2×Q16×C61 | C2×C4 | semidirect |
| 62. C2×D8×C61 | C2×C4 | semidirect |
| 198. C2×#135 | #6923 | semidirect |
| 215. C61 | #11685 | semidirect |
| 220. C2×Q16 | C2×#6923 | semidirect |
| 222. C2×D8 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840659 | 2 |
| C2×#16840630 | 2 |
| #21460791 | 2 |
| #21460789 | 2 |
| #21455424 | 2 |
| #11685 | 61 |