Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
204 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 74 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. #21462209 | C2 | semidirect |
| 2. #21460846 | C2 | semidirect |
| 3. #21460783 | C2 | semidirect |
| 4. #21460736 | C2 | semidirect |
| 27. Q32×C61 | C8 | semidirect |
| 28. SD32×C61 | C8 | semidirect |
| 29. D16×C61 | C8 | semidirect |
| 83. C61 | #12068 | semidirect |
| 86. Q32 | #92420 | semidirect |
| 87. SD32 | #92420 | semidirect |
| 88. D16 | #92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462209 | 2 |
| #21460846 | 2 |
| #21460783 | 2 |
| #21460736 | 2 |
| #21447705 | 2 |
| #12068 | 61 |