Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
338 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 12. C4×#92420 | C8 | semidirect |
| 19. C4×#92418 | C8 | semidirect |
| 23. C4×C8×C61 | C8 | semidirect |
| 95. C61 | #7014 | semidirect |
| 109. C4×C8 | #92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461533 | 2 |
| #21445564 | 2 |
| #7014 | 61 |