Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
642 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 211 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. #21446780 | C2 | semidirect |
| 4. #21445976 | C2 | semidirect |
| 5. C2×C82×C61 | C2 | semidirect |
| 10. #16840135 | C4 | semidirect |
| 65. C2×C8×C61 | SD16 | semidirect |
| 102. C8×C61 | #102 | semidirect |
| 124. C2×C82 | D61 | semidirect |
| 143. C61 | #9820 | semidirect |
| 190. C2×C8 | #11758190 | semidirect |
| 228. C8 | #14519699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840135 | 2 |
| #21446780 | 2 |
| #21446625 | 2 |
| #21445976 | 2 |
| C2×C82×C61 | 2 |
| #9820 | 61 |