Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 3. C2×#16840655 | C2 | semidirect |
| 4. #21460861 | C2 | semidirect |
| 7. C2×#14519851 | C4 | semidirect |
| 11. C22×#11758187 | C4 | semidirect |
| 12. C22⋊#11758187 | C4 | semidirect |
| 13. C22⋊#11758187 | C4 | semidirect |
| 77. #11758187 | C22⋊C4 | semidirect |
| 115. C22×C61 | #347 | semidirect |
| 149. C61 | #12616 | semidirect |
| 244. C22 | #16840655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519851 | 2 |
| #21462046 | 2 |
| C2×#16840655 | 2 |
| #21460861 | 2 |
| #21445598 | 2 |
| #12616 | 61 |