Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
222 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. #21460928 | C2 | direct (N × H) |
| 7. #16840695 | C4 | semidirect |
| 9. C2×#14519827 | C4 | semidirect |
| 13. #16839595 | C4 | semidirect |
| 15. C2×#14519683 | C4 | semidirect |
| 16. C2×C32×C61 | C4 | semidirect |
| 24. #14519827 | C2×C4 | semidirect |
| 31. #14519683 | C2×C4 | semidirect |
| 33. C32×C61 | C2×C4 | semidirect |
| 80. C2×C61 | #1398 | semidirect |
| 93. C2×C32 | #6923 | semidirect |
| 96. C61 | C2×#1398 | semidirect |
| 113. C32 | C2×#6923 | semidirect |
| 157. C2 | #21460928 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840695 | 2 |
| C2×#16840649 | 2 |
| #21460928 | 2 |
| C2×#16839595 | 2 |
| C2×#1398 | 61 |