Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
906 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 211 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. #21456394 | C2 | semidirect |
| 2. #21456247 | C2 | semidirect |
| 3. #21445491 | C2 | semidirect |
| 4. #21445488 | C2 | semidirect |
| 5. #21445486 | C2 | semidirect |
| 6. #21445483 | C2 | semidirect |
| 7. C2×#16839483 | C2 | semidirect |
| 8. C61×#3147 | C2 | semidirect |
| 80. C2×C8×C61 | D8 | semidirect |
| 136. #3147 | D61 | semidirect |
| 169. C61 | #19616 | semidirect |
| 225. C2×C8 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456394 | 2 |
| #21456247 | 2 |
| #21445491 | 2 |
| #21445488 | 2 |
| #21445486 | 2 |
| #21445483 | 2 |
| C2×#16839483 | 2 |
| C61×#3147 | 2 |
| #19616 | 61 |