Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
488 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 1. C22×#14519716 | C2 | semidirect |
| 3. C2×#16839569 | C2 | semidirect |
| 4. #21445854 | C2 | semidirect |
| 5. #21443916 | C2 | semidirect |
| 6. #21443915 | C2 | semidirect |
| 7. C2×C61×#359 | C2 | semidirect |
| 45. C2×#11758185 | D4 | semidirect |
| 65. C2×C16×C61 | D4 | semidirect |
| 178. C2×#359 | D61 | semidirect |
| 207. C61 | #13064 | semidirect |
| 239. C2×C16 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519716 | 2 |
| #21455396 | 2 |
| C2×#16839569 | 2 |
| #21445854 | 2 |
| #21443916 | 2 |
| #21443915 | 2 |
| C2×C61×#359 | 2 |
| #13064 | 61 |