Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
374 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 374 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. #21446592 | C2 | semidirect |
| 3. #21444595 | C2 | semidirect |
| 4. #21444569 | C2 | semidirect |
| 7. C61×#1292 | C2 | semidirect |
| 158. #1292 | D61 | semidirect |
| 182. C61 | #10603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446658 | 2 |
| #21446592 | 2 |
| #21444595 | 2 |
| #21444569 | 2 |
| #21444488 | 2 |
| C2×#16839505 | 2 |
| C61×#1292 | 2 |
| #10603 | 61 |