Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
930 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 219 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×#14519721 | C2 | semidirect |
| 2. C22×#14519718 | C2 | semidirect |
| 3. C2×#16840146 | C2 | semidirect |
| 4. #21448083 | C2 | direct (N × H) |
| 5. C2×#16839538 | C2 | semidirect |
| 6. C2×C61×#493 | C2 | semidirect |
| 12. C2×#14519721 | C22 | semidirect |
| 14. C2×#14519718 | C22 | semidirect |
| 17. #16840146 | C22 | semidirect |
| 18. #16839538 | C22 | semidirect |
| 23. C61×#493 | C22 | semidirect |
| 40. C2×#11758185 | D4 | semidirect |
| 93. #11758185 | C2×D4 | semidirect |
| 140. C2×#493 | D61 | semidirect |
| 144. C2×C61 | #2250 | semidirect |
| 163. #493 | C2×D61 | semidirect |
| 166. C61 | C2×#2250 | semidirect |
| 280. C2 | #21448083 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519721 | 2 |
| C22×#14519718 | 2 |
| C2×#16840146 | 2 |
| #21448083 | 2 |
| C2×#16839538 | 2 |
| C2×C61×#493 | 2 |
| C2×#2250 | 61 |