Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #21446607 | C2 | semidirect |
| 5. #21443930 | C2 | semidirect |
| 6. #21443907 | C2 | semidirect |
| 7. C2×C61×#368 | C2 | semidirect |
| 17. #16839570 | C4 | semidirect |
| 137. C2×#368 | D61 | semidirect |
| 164. C61 | #12947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454735 | 2 |
| #21447546 | 2 |
| C2×#16839570 | 2 |
| #21446607 | 2 |
| #21443930 | 2 |
| #21443907 | 2 |
| C2×C61×#368 | 2 |
| #12947 | 61 |