Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
372 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21444565 | C2 | semidirect |
| 3. C2×#16839512 | C2 | semidirect |
| 6. #21443670 | C2 | semidirect |
| 7. C61×#1283 | C2 | semidirect |
| 155. #1283 | D61 | semidirect |
| 181. C61 | #8607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454464 | 2 |
| #21444565 | 2 |
| C2×#16839512 | 2 |
| #21444207 | 2 |
| #21444204 | 2 |
| #21443670 | 2 |
| C61×#1283 | 2 |
| #8607 | 61 |