Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21447656 | C2 | semidirect |
| 3. #21447655 | C2 | semidirect |
| 4. #21443894 | C2 | semidirect |
| 5. #21443793 | C2 | semidirect |
| 6. #21443736 | C2 | semidirect |
| 7. C61×#1335 | C2 | semidirect |
| 25. #14519723 | C8 | semidirect |
| 26. #14519721 | C8 | semidirect |
| 27. #14519720 | C8 | semidirect |
| 28. #14519718 | C8 | semidirect |
| 104. #1335 | D61 | semidirect |
| 125. C61 | #12047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447698 | 2 |
| #21447656 | 2 |
| #21447655 | 2 |
| #21443894 | 2 |
| #21443793 | 2 |
| #21443736 | 2 |
| C61×#1335 | 2 |
| #12047 | 61 |