Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
516 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 3. C4×C8×#6923 | C2 | semidirect |
| 4. #21461031 | C2 | semidirect |
| 5. #21460651 | C2 | semidirect |
| 6. #21460646 | C2 | semidirect |
| 8. #16840812 | C4 | semidirect |
| 9. #16840797 | C4 | semidirect |
| 25. #16839494 | C4 | semidirect |
| 26. #16839492 | C4 | semidirect |
| 27. D4⋊#92418 | C4 | semidirect |
| 28. C61×D4⋊C8 | C4 | semidirect |
| 88. C4×#6923 | M16 | semidirect |
| 142. #92420 | #104 | semidirect |
| 197. D4⋊C8 | #6923 | semidirect |
| 200. C61 | #8194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462631 | 2 |
| C4×#14519841 | 2 |
| C4×C8×#6923 | 2 |
| #21461031 | 2 |
| #21460651 | 2 |
| #21460646 | 2 |
| #21444198 | 2 |
| #8194 | 61 |