Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
438 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 1. C2×#16840688 | C2 | semidirect |
| 3. #21460877 | C2 | semidirect |
| 10. C22×#11758185 | C4 | semidirect |
| 12. C2×C16×D61 | C4 | semidirect |
| 13. C2×C16×D61 | C4 | semidirect |
| 16. C22×C16×C61 | C4 | semidirect |
| 68. C16×C61 | C22⋊C4 | semidirect |
| 70. #11758185 | C22⋊C4 | semidirect |
| 102. C22×C61 | #366 | semidirect |
| 108. C2×D61 | #366 | semidirect |
| 137. C22×C16 | #6923 | semidirect |
| 142. C61 | #12834 | semidirect |
| 196. C16 | C22⋊#6923 | semidirect |
| 236. C22 | #16840688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840688 | 2 |
| #21461696 | 2 |
| #21460877 | 2 |
| C22×C16×D61 | 2 |
| #12834 | 61 |