Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
418 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 10. #16840653 | C4 | direct (N × H) |
| 11. #16840651 | C4 | semidirect |
| 12. C4×#11758187 | C4 | semidirect |
| 15. #16839537 | C4 | semidirect |
| 16. C4×#11758185 | C4 | semidirect |
| 17. C4×C16×C61 | C4 | semidirect |
| 54. #11758187 | C42 | semidirect |
| 55. C16×C61 | C42 | semidirect |
| 56. #11758185 | C42 | semidirect |
| 77. C4×C61 | #347 | semidirect |
| 101. C4×C16 | #6923 | semidirect |
| 102. C61 | C4×#347 | semidirect |
| 141. C16 | C4×#6923 | semidirect |
| 163. C4 | #16840653 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840653 | 2 |
| C4×#14519852 | 2 |
| C4×#14519831 | 2 |
| C4×#14519716 | 2 |
| C4×#347 | 61 |