Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
418 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 204 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 |
|---|---|---|
| 5. #16840654 | C4 | direct (N × H) |
| 6. #16840650 | C4 | semidirect |
| 7. C4×#11758187 | C4 | semidirect |
| 42. #11758187 | C42 | semidirect |
| 62. C4×C61 | #347 | semidirect |
| 81. C61 | C4×#347 | semidirect |
| 130. C4 | #16840654 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840654 | 2 |
| C4×#14519851 | 2 |
| C4×#14519688 | 2 |
| C4×#347 | 61 |