Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
246 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 77 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. #21444642 | C2 | semidirect |
| 3. #21443785 | C2 | semidirect |
| 4. #21443739 | C2 | semidirect |
| 5. C61×#1368 | C2 | semidirect |
| 19. D976 | C8 | semidirect |
| 39. D488 | C2×C8 | semidirect |
| 42. C16×C61 | C2×C8 | semidirect |
| 68. #1368 | D61 | semidirect |
| 84. C61 | #12067 | semidirect |
| 112. C16 | C8×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447696 | 2 |
| #21444642 | 2 |
| #21443785 | 2 |
| #21443739 | 2 |
| C61×#1368 | 2 |
| #12067 | 61 |