Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #21446560 | C2 | semidirect |
| 5. #21443924 | C2 | semidirect |
| 6. #21443902 | C2 | semidirect |
| 7. C61×#2159 | C2 | semidirect |
| 19. #16839573 | C4 | semidirect |
| 52. #14519709 | C2×C4 | semidirect |
| 64. M32×C61 | C2×C4 | semidirect |
| 113. Dic244 | C4⋊C4 | semidirect |
| 115. D488 | C4⋊C4 | semidirect |
| 177. #2159 | D61 | semidirect |
| 209. C61 | #12943 | semidirect |
| 236. M32 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454619 | 2 |
| C2×#16839573 | 2 |
| #21447529 | 2 |
| #21446560 | 2 |
| #21443924 | 2 |
| #21443902 | 2 |
| C61×#2159 | 2 |
| #12943 | 61 |