Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
802 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21446654 | C2 | semidirect |
| 3. #21445763 | C2 | semidirect |
| 4. #21444334 | C2 | semidirect |
| 5. #21443725 | C2 | semidirect |
| 6. #21443705 | C2 | semidirect |
| 7. C61×#2339 | C2 | semidirect |
| 8. C2×#14519802 | C4 | semidirect |
| 14. #16839763 | C4 | semidirect |
| 29. C22×D244 | C2×C4 | semidirect |
| 35. C2×#11758194 | C2×C4 | semidirect |
| 40. C2×C4⋊Dic61 | C2×C4 | semidirect |
| 160. D4×C61 | #99 | semidirect |
| 231. #2339 | D61 | semidirect |
| 267. C61 | #9365 | semidirect |
| 404. D4 | #14519691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455071 | 2 |
| #21446654 | 2 |
| #21445763 | 2 |
| #21444334 | 2 |
| #21443725 | 2 |
| #21443705 | 2 |
| C61×#2339 | 2 |
| #9365 | 61 |