Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#16839586 | C2 | semidirect |
| 4. #21446599 | C2 | semidirect |
| 5. #21443922 | C2 | semidirect |
| 6. #21443905 | C2 | semidirect |
| 15. #16839569 | C4 | semidirect |
| 167. C61 | #12948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839586 | 2 |
| C2×#16839572 | 2 |
| #21447547 | 2 |
| #21446599 | 2 |
| #21443922 | 2 |
| #21443905 | 2 |
| C61×#2957 | 2 |
| #12948 | 61 |