Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
662 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21448990 | C2 | semidirect |
| 3. #21446644 | C2 | semidirect |
| 4. C2×#16839501 | C2 | semidirect |
| 5. #21443701 | C2 | semidirect |
| 6. #21443700 | C2 | semidirect |
| 7. C61×#1961 | C2 | semidirect |
| 12. #16840149 | C4 | semidirect |
| 59. #14519688 | C2×C4 | semidirect |
| 71. #127×C61 | C2×C4 | semidirect |
| 246. #1961 | D61 | semidirect |
| 281. C61 | #9001 | semidirect |
| 300. #127 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840149 | 2 |
| #21448990 | 2 |
| #21446644 | 2 |
| C2×#16839501 | 2 |
| #21443701 | 2 |
| #21443700 | 2 |
| C61×#1961 | 2 |
| #9001 | 61 |