Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
190 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 10. #16839602 | C4 | direct (N × H) |
| 74. C4×C61 | Q64 | semidirect |
| 101. C61 | C4×Q64 | semidirect |
| 157. C4 | #16839602 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839602 | 2 |
| C4×Dic488 | 2 |
| #21444018 | 2 |
| #21444000 | 2 |
| #21443999 | 2 |
| C4×#14519683 | 2 |
| C4×Q32×C61 | 2 |
| C4×Q64 | 61 |