Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
566 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 101 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×#14519720 | C2 | semidirect |
| 3. C2×#16839576 | C2 | semidirect |
| 4. C2×#16839569 | C2 | semidirect |
| 5. #21446735 | C2 | semidirect |
| 6. #21443909 | C2 | semidirect |
| 7. C2×C61×#510 | C2 | semidirect |
| 52. C2×#11758185 | D4 | semidirect |
| 71. C2×Q16×C61 | D4 | semidirect |
| 78. M32×C61 | D4 | semidirect |
| 196. C2×#510 | D61 | semidirect |
| 232. C61 | #13338 | semidirect |
| 248. C2×Q16 | C22⋊D61 | semidirect |
| 271. M32 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519720 | 2 |
| #21456306 | 2 |
| C2×#16839576 | 2 |
| C2×#16839569 | 2 |
| #21446735 | 2 |
| #21443909 | 2 |
| C2×C61×#510 | 2 |
| #13338 | 61 |