Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
282 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 21. #16839589 | C4 | semidirect |
| 22. #16839588 | C4 | semidirect |
| 23. #16839587 | C4 | semidirect |
| 24. C61×#367 | C4 | semidirect |
| 84. C16×C61 | C4⋊C4 | semidirect |
| 85. #11758185 | C4⋊C4 | semidirect |
| 149. #367 | #6923 | semidirect |
| 156. C61 | #13174 | semidirect |
| 217. C16 | C4⋊#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840687 | 2 |
| C2×#16840652 | 2 |
| #21461928 | 2 |
| #21461924 | 2 |
| #21460893 | 2 |
| #21460890 | 2 |
| #21447606 | 2 |
| #13174 | 61 |