Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
438 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #21454890 | C2 | semidirect |
| 3. #21444442 | C2 | semidirect |
| 4. #21444170 | C2 | semidirect |
| 5. #21443731 | C2 | semidirect |
| 6. #21443681 | C2 | semidirect |
| 7. C61×#1553 | C2 | semidirect |
| 162. #1553 | D61 | semidirect |
| 192. C61 | #9333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456802 | 2 |
| #21454890 | 2 |
| #21444442 | 2 |
| #21444170 | 2 |
| #21443731 | 2 |
| #21443681 | 2 |
| C61×#1553 | 2 |
| #9333 | 61 |