Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
408 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 2. C2×#16839586 | C2 | semidirect |
| 5. #21446558 | C2 | semidirect |
| 6. #21443898 | C2 | semidirect |
| 7. C61×#1387 | C2 | semidirect |
| 19. #16839565 | C4 | semidirect |
| 20. #16839562 | C4 | semidirect |
| 92. Dic244 | C4⋊C4 | semidirect |
| 94. D488 | C4⋊C4 | semidirect |
| 155. #1387 | D61 | semidirect |
| 180. C61 | #12955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839883 | 2 |
| C2×#16839586 | 2 |
| C2×#16839573 | 2 |
| #21447529 | 2 |
| #21446558 | 2 |
| #21443898 | 2 |
| C61×#1387 | 2 |
| #12955 | 61 |