Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16840017 | C2 | semidirect |
| 3. C2×#16839572 | C2 | semidirect |
| 4. #21447539 | C2 | semidirect |
| 5. C2×#16839543 | C2 | semidirect |
| 6. #21443925 | C2 | semidirect |
| 7. C2×C61×#510 | C2 | semidirect |
| 56. #14519709 | D4 | semidirect |
| 72. C2×Q16×C61 | D4 | semidirect |
| 79. M32×C61 | D4 | semidirect |
| 206. C2×#510 | D61 | semidirect |
| 242. C61 | #13317 | semidirect |
| 256. C2×Q16 | C22⋊D61 | semidirect |
| 283. M32 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455424 | 2 |
| C2×#16840017 | 2 |
| C2×#16839572 | 2 |
| #21447539 | 2 |
| C2×#16839543 | 2 |
| #21443925 | 2 |
| C2×C61×#510 | 2 |
| #13317 | 61 |