Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
834 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 179 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×#16840193 | C2 | semidirect |
| 2. #21456248 | C2 | semidirect |
| 3. #21456246 | C2 | semidirect |
| 4. #21448079 | C2 | semidirect |
| 5. #21448075 | C2 | semidirect |
| 6. #21448071 | C2 | semidirect |
| 7. #21448068 | C2 | semidirect |
| 8. C4×C16×D61 | C2 | semidirect |
| 9. C61×#2248 | C2 | semidirect |
| 65. C16×D61 | D4 | semidirect |
| 160. C4×C61 | #508 | semidirect |
| 171. #2248 | D61 | semidirect |
| 206. C61 | #33713 | semidirect |
| 333. C4 | #16840193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840193 | 2 |
| #21456248 | 2 |
| #21456246 | 2 |
| #21448079 | 2 |
| #21448075 | 2 |
| #21448071 | 2 |
| #21448068 | 2 |
| C4×C16×D61 | 2 |
| C61×#2248 | 2 |
| #33713 | 61 |