Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
698 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 148 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. #21461734 | C2 | semidirect |
| 2. #21461533 | C2 | semidirect |
| 3. C2×D4⋊#92420 | C2 | semidirect |
| 21. C4×#92420 | D4 | semidirect |
| 37. #127×C61 | C8 | semidirect |
| 142. C61 | #9642 | semidirect |
| 149. #127 | #92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461734 | 2 |
| #21461533 | 2 |
| C2×D4⋊#92420 | 2 |
| #127×Dic61 | 2 |
| #9642 | 61 |