Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
388 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21444580 | C2 | semidirect |
| 3. #21444580 | C2 | semidirect |
| 6. #21443730 | C2 | semidirect |
| 7. C61×#1307 | C2 | semidirect |
| 146. #1307 | D61 | semidirect |
| 171. C61 | #8634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454530 | 2 |
| #21444580 | 2 |
| #21444453 | 2 |
| #21443730 | 2 |
| C61×#1307 | 2 |
| #8634 | 61 |