Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 2. #21445910 | C2 | semidirect |
| 3. #21445897 | C2 | semidirect |
| 5. #21443724 | C2 | semidirect |
| 6. #21443696 | C2 | semidirect |
| 10. #16840090 | C4 | semidirect |
| 12. #16840073 | C4 | semidirect |
| 247. C61 | #9521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455739 | 2 |
| #21445910 | 2 |
| #21445897 | 2 |
| #21444362 | 2 |
| #21443724 | 2 |
| #21443696 | 2 |
| C61×#2976 | 2 |
| #9521 | 61 |