Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
330 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#16839595 | C2 | semidirect |
| 3. #21447600 | C2 | semidirect |
| 4. #21443998 | C2 | semidirect |
| 5. #21443997 | C2 | semidirect |
| 6. #21443996 | C2 | semidirect |
| 7. C61×#1415 | C2 | semidirect |
| 12. D16×D61 | C4 | semidirect |
| 16. C2×#14519683 | C22 | semidirect |
| 18. #16839588 | C22 | semidirect |
| 20. C2×C32×C61 | C22 | semidirect |
| 21. C61×#366 | C22 | semidirect |
| 110. #1415 | D61 | semidirect |
| 127. C2×C32 | C2×D61 | semidirect |
| 130. #366 | C2×D61 | semidirect |
| 131. C61 | #13617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D61 | 2 |
| C2×#16839595 | 2 |
| #21447600 | 2 |
| #21443998 | 2 |
| #21443997 | 2 |
| #21443996 | 2 |
| C61×#1415 | 2 |
| #13617 | 61 |