Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
390 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 86 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×#16840689 | C2 | semidirect |
| 4. #107×#6923 | C2 | semidirect |
| 5. #21460876 | C2 | semidirect |
| 6. (C2×#6923)⋊C16 | C2 | semidirect |
| 21. #16839564 | C4 | semidirect |
| 22. #16839563 | C4 | semidirect |
| 23. #16839562 | C4 | semidirect |
| 24. C61×#357 | C4 | semidirect |
| 205. #357 | #6923 | semidirect |
| 207. C61 | #13131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840689 | 2 |
| C2×#16840674 | 2 |
| #21461966 | 2 |
| #107×#6923 | 2 |
| #21460876 | 2 |
| (C2×#6923)⋊C16 | 2 |
| #357×D61 | 2 |
| #13131 | 61 |