Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
768 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 2. #21460908 | C2 | semidirect |
| 3. #21460907 | C2 | semidirect |
| 7. #16840742 | C4 | semidirect |
| 11. D61⋊#99 | C4 | semidirect |
| 13. C22×#11758189 | C4 | semidirect |
| 14. C2×M16×D61 | C4 | semidirect |
| 16. #16839729 | C4 | semidirect |
| 20. C61×#408 | C4 | semidirect |
| 31. #14519835 | C2×C4 | semidirect |
| 44. C2×#11758194 | C2×C4 | semidirect |
| 50. C22×#92418 | C2×C4 | semidirect |
| 56. C2×M16×C61 | C2×C4 | semidirect |
| 57. C22×C8×C61 | C2×C4 | semidirect |
| 220. #408 | #6923 | semidirect |
| 222. C61 | #12577 | semidirect |
| 242. C2×M16 | C2×#6923 | semidirect |
| 245. C22×C8 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#410 | 2 |
| #21460908 | 2 |
| #21460907 | 2 |
| #21454261 | 2 |
| #12577 | 61 |