Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21448727 | C2 | semidirect |
| 3. #21444314 | C2 | semidirect |
| 4. #21444211 | C2 | semidirect |
| 5. #21443721 | C2 | semidirect |
| 6. #21443677 | C2 | semidirect |
| 7. C61×#1517 | C2 | semidirect |
| 12. #16839964 | C4 | semidirect |
| 13. #16839954 | C4 | semidirect |
| 51. C4⋊#92418 | C2×C4 | semidirect |
| 60. C4⋊Q8×C61 | C2×C4 | semidirect |
| 61. #127×C61 | C2×C4 | semidirect |
| 210. #1517 | D61 | semidirect |
| 243. C61 | #9179 | semidirect |
| 253. C4⋊Q8 | C4×D61 | semidirect |
| 254. #127 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455279 | 2 |
| #21448727 | 2 |
| #21444314 | 2 |
| #21444211 | 2 |
| #21443721 | 2 |
| #21443677 | 2 |
| C61×#1517 | 2 |
| #9179 | 61 |