Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#16839571 | C2 | semidirect |
| 3. #21447532 | C2 | semidirect |
| 4. #21447531 | C2 | semidirect |
| 5. #21446563 | C2 | semidirect |
| 6. #21443902 | C2 | semidirect |
| 7. C2×C61×#360 | C2 | semidirect |
| 77. #106×C61 | D4 | semidirect |
| 209. C2×#360 | D61 | semidirect |
| 242. C61 | #13410 | semidirect |
| 288. #106 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456262 | 2 |
| C2×#16839571 | 2 |
| #21447532 | 2 |
| #21447531 | 2 |
| #21446563 | 2 |
| #21443902 | 2 |
| C2×C61×#360 | 2 |
| #13410 | 61 |