Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
676 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 143 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×#16840195 | C2 | semidirect |
| 2. #21457539 | C2 | semidirect |
| 3. #21447907 | C2 | semidirect |
| 4. #21447861 | C2 | semidirect |
| 5. #21447758 | C2 | semidirect |
| 6. C4×D976 | C2 | semidirect |
| 7. C16×D244 | C2 | semidirect |
| 8. C61×#2247 | C2 | semidirect |
| 42. D976 | D4 | semidirect |
| 122. C4×C61 | #508 | semidirect |
| 129. #2247 | D61 | semidirect |
| 160. C61 | #33849 | semidirect |
| 255. C4 | #16840195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840195 | 2 |
| #21457539 | 2 |
| #21447907 | 2 |
| #21447861 | 2 |
| #21447758 | 2 |
| C4×D976 | 2 |
| C16×D244 | 2 |
| C61×#2247 | 2 |
| #33849 | 61 |