Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
198 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 62. #11758185 | Q16 | semidirect |
| 117. C61 | #12459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448099 | 2 |
| Q8×#11758185 | 2 |
| #21445213 | 2 |
| #21443892 | 2 |
| #21443877 | 2 |
| #21443875 | 2 |
| C61×#1676 | 2 |
| #12459 | 61 |