Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
334 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 14. #16839537 | C4 | semidirect |
| 15. C4×#11758185 | C4 | semidirect |
| 16. C4×C16×C61 | C4 | semidirect |
| 56. C16×C61 | C4⋊C4 | semidirect |
| 57. #11758185 | C4⋊C4 | semidirect |
| 81. C4×C61 | #365 | semidirect |
| 106. C4×C16 | #6923 | semidirect |
| 107. C61 | #12903 | semidirect |
| 148. C16 | C4⋊#6923 | semidirect |
| 174. C4 | #16840687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840687 | 2 |
| #21461758 | 2 |
| #21461754 | 2 |
| C4×#14519716 | 2 |
| #12903 | 61 |