Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
486 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 184 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×#16840650 | C2 | semidirect |
| 4. #21460857 | C2 | semidirect |
| 7. C22×#11758187 | C4 | semidirect |
| 11. C22⋊#11758187 | C4 | semidirect |
| 65. #11758187 | C22⋊C4 | semidirect |
| 92. C22×C61 | #346 | semidirect |
| 124. C61 | #12611 | semidirect |
| 198. C22 | #16840650 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11758187 | 2 |
| C2×C22⋊#11758187 | 2 |
| C2×#16840650 | 2 |
| #21460857 | 2 |
| C22⋊C4×#92418 | 2 |
| #12611 | 61 |