Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
500 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 3. #21443643 | C2 | semidirect |
| 4. #21443641 | C2 | semidirect |
| 204. C61 | #7711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454129 | 2 |
| #21445799 | 2 |
| #21443643 | 2 |
| #21443641 | 2 |
| C61×#1728 | 2 |
| #7711 | 61 |