Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
346 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21458166 | C2 | semidirect |
| 2. #21447851 | C2 | semidirect |
| 3. #21445171 | C2 | semidirect |
| 4. #21443874 | C2 | semidirect |
| 5. #21443781 | C2 | semidirect |
| 6. #21443775 | C2 | semidirect |
| 7. C61×#2240 | C2 | semidirect |
| 108. D244 | D16 | semidirect |
| 139. #2240 | D61 | semidirect |
| 168. C61 | #12340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458166 | 2 |
| #21447851 | 2 |
| #21445171 | 2 |
| #21443874 | 2 |
| #21443781 | 2 |
| #21443775 | 2 |
| C61×#2240 | 2 |
| #12340 | 61 |