Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
540 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. C22×#14519721 | C2 | semidirect |
| 3. #21455475 | C2 | semidirect |
| 4. C2×#16839579 | C2 | semidirect |
| 5. C2×#16839547 | C2 | semidirect |
| 6. #21443914 | C2 | semidirect |
| 7. C61×#2140 | C2 | semidirect |
| 192. #2140 | D61 | semidirect |
| 222. C61 | #13320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519721 | 2 |
| C2×#16840029 | 2 |
| #21455475 | 2 |
| C2×#16839579 | 2 |
| C2×#16839547 | 2 |
| #21443914 | 2 |
| C61×#2140 | 2 |
| #13320 | 61 |