Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
392 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #21443927 | C2 | semidirect |
| 5. #21443919 | C2 | semidirect |
| 6. #21443918 | C2 | semidirect |
| 7. C61×#1387 | C2 | semidirect |
| 12. #16839809 | C4 | semidirect |
| 149. #1387 | D61 | semidirect |
| 172. C61 | #12875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839809 | 2 |
| C2×#16839543 | 2 |
| #21445853 | 2 |
| #21443927 | 2 |
| #21443919 | 2 |
| #21443918 | 2 |
| C61×#1387 | 2 |
| #12875 | 61 |