Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1074 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 203 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×#16840141 | C2 | semidirect |
| 3. C2×#16840053 | C2 | semidirect |
| 4. #21444965 | C2 | direct (N × H) |
| 5. C2×#16839489 | C2 | semidirect |
| 6. C2×C61×#333 | C2 | semidirect |
| 17. #16840141 | C22 | semidirect |
| 19. #16840053 | C22 | semidirect |
| 23. #16839489 | C22 | semidirect |
| 26. C61×#333 | C22 | semidirect |
| 156. C2×#333 | D61 | semidirect |
| 158. C2×C61 | #1634 | semidirect |
| 180. #333 | C2×D61 | semidirect |
| 182. C61 | C2×#1634 | semidirect |
| 308. C2 | #21444965 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840478 | 2 |
| C2×#16840141 | 2 |
| C2×#16840053 | 2 |
| #21444965 | 2 |
| C2×#16839489 | 2 |
| C2×C61×#333 | 2 |
| C2×#1634 | 61 |