Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1470 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 1470 conjugacy classes of subgroups — too many to draw. Only its 320 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×D61⋊C16 | C2 | semidirect |
| 2. C22×#14519846 | C2 | semidirect |
| 3. C2×#16840674 | C2 | direct (N × H) |
| 7. C2×D61⋊C16 | C22 | semidirect |
| 10. C2×#14519846 | C22 | semidirect |
| 11. #16840674 | C22 | direct (N × H) |
| 13. C22×D488 | C4 | semidirect |
| 17. C2×D8×D61 | C4 | semidirect |
| 20. C22×D8×C61 | C4 | semidirect |
| 25. D61⋊C16 | C23 | semidirect |
| 28. #14519846 | C23 | semidirect |
| 38. C2×D488 | C2×C4 | semidirect |
| 44. D8×D61 | C2×C4 | semidirect |
| 53. C2×D8×C61 | C2×C4 | semidirect |
| 84. D8×C61 | C22×C4 | semidirect |
| 92. D488 | C22×C4 | semidirect |
| 137. C22×C61 | #357 | semidirect |
| 144. C2×D61 | #357 | semidirect |
| 159. C2×C61 | C2×#357 | semidirect |
| 162. D61 | C2×#357 | semidirect |
| 172. C22×D8 | #6923 | semidirect |
| 181. C61 | C22×#357 | semidirect |
| 202. C2×D8 | C2×#6923 | semidirect |
| 247. D8 | C22×#6923 | semidirect |
| 307. C22 | #16840674 | direct (N × H) |
| 319. C2 | C2×#16840674 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D61⋊C16 | 2 |
| C22×#14519846 | 2 |
| C2×#16840674 | 2 |
| C22×D8×D61 | 2 |
| C22×#357 | 61 |